研究者総覧

上島　芳倫 (カミジマ　ヨシノリ)

情報連携学部情報連携学科　助教

Last Updated :2025/04/19

研究者情報

学位

博士 (理学)（2021年03月北海道大学）

修士（理学）（2017年03月北海道大学）

ホームページURL

https://ykami.gitlab.io/webpage/

科研費研究者番号

30912646

ORCID ID

https://orcid.org/0000-0003-3037-8250

J-Global ID

202001014579618911

研究キーワード

数理物理統計力学確率論相転移臨界現象レース展開自己回避歩行パーコレーションスピン系

研究分野

自然科学一般 / 基礎解析学 / 確率論

自然科学一般 / 数理物理、物性基礎 / 統計物理学

経歴

2024年03月 - 現在東洋大学情報連携学部助教

2021年08月 - 2024年03月國家理論科學研究中心ポスドク

2021年04月 - 2021年08月北海道大学数理・データサイエンス教育研究センター学術研究員

学歴

2017年04月 - 2021年03月北海道大学大学院理学院数学専攻

2015年04月 - 2017年03月北海道大学大学院理学院数学専攻

2011年04月 - 2015年03月新潟大学理学部物理学科

2008年04月 - 2011年03月長野県伊那北高等学校普通科

所属学協会

一般社団法人日本数学会

研究活動情報

論文

Mixing Time and Simulated Annealing for the Stochastic Cellular Automata
Bruno Hideki Fukushima-Kimura; 半田悟; 鎌倉雄洋; 上島芳倫; 川村一志; 坂井哲
Journal of Statistical Physics 190 4 Springer Science and Business Media LLC 2023年03月 [査読有り]

Mean-field behavior of Nearest-Neighbor Oriented Percolation on the BCC Lattice Above 8 + 1 Dimensions
陳隆奇; 半田悟; 上島芳倫
Mathematical Physics, Analysis and Geometry 26 1 Springer Science and Business Media LLC 2023年02月 [査読有り]

Stochastic Optimization
Bruno Hideki Fukushima-Kimura; Yoshinori Kamijima; Kazushi Kawamura; Akira Sakai
Transactions of the Institute of Systems, Control and Information Engineers 36 1 9 - 16 2023年01月

Stochastic optimization via parallel dynamics: rigorous results and simulations
Bruno Hideki Fukushima-Kimura; 上島芳倫; 川村一志; 坂井哲
Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 2022 65 - 71 The Institute of Systems, Control and Information Engineers 2022年03月 [査読有り]

パーコレーション模型に対する平均場臨界現象
上島芳倫
北海道大学 2021年03月

A Survey on the Lace Expansion for the Nearest-neighbor Models on the BCC Lattice
半田悟; 上島芳倫; 坂井哲
Taiwanese Journal of Mathematics 24 3 723 - 784 2020年06月 [査読有り]

講演・口頭発表等

長距離相互作用を持つ自己回避歩行に対する局所極限定理 [通常講演]
上島芳倫
日本数学会2024年度秋季総合分科会 2024年09月口頭発表（一般）大阪大学
自己回避歩行はランダムウォークに自分自身と交わらないという条件を加えた模型である．言い換えると，或るグラフ上の経路を考えた時，ランダムウォークでは再度同じ頂点を踏むことが起こり得るが，自己回避歩行では同じ頂点を踏まない経路のみが実現される．本研究では一歩の遷移確率 $D\colon \mathbb{Z}^d \to [0, 1]$ を特に裾の重い分布に取る場合を考える．遷移確率 $D$ の台が有限の時には，中心極限定理が成り立つことが知られている~[van der Hofstad and Slade (2002) PTRF]．その文献では，球内での平均値を取ることによって，或る種の局所極限定理をも証明している．また，$D$ が裾の重いspread-out模型の場合には，自己回避歩行の二点関数が冪的に減衰することが示されている~[Chen and Sakai (2019) CMP]．本講演では，$D$ が裾の重いspread-out模型の場合に，本来の意味での局所極限定理を証明する試みについて説明する．本研究は陳隆奇（国立政治大学，台湾）と千野由喜（国立陽明交通大学，台湾）との共同研究である．

時空間でのランダムカレント表現に基づくIsing模型に対するレース展開の導出 [通常講演]
上島芳倫
東京確率論セミナー 2024年07月口頭発表（一般）東京大学大学院数理科学研究科数理科学研究科棟（駒場）中島秀太;佐々田槙子

レース展開は平均場臨界現象を解析する為の強力な手法の一つである．レース展開を用いると，例えば臨界点の漸近展開が得られ，それは現在までに自己回避歩行・無向パーコレーション・有効パーコレーション・コンタクトプロセス等で示されている．本研究の目的は，量子Ising模型に対するレース展開を導出し，それによって量子Ising模型の臨界点の評価を得ることである．頂点集合 $\Lambda$ 上のスピン配置 $\vec{\sigma} \in \{-1, +1\}^{\Lambda}$ がGibbs分布に従って実現されるという数理模型を古典Ising模型という．量子Ising模型とは，その古典Ising模型のスピン配置空間の代わりに対応するテンソル空間 $(\mathbb{C}^2)^{\otimes \Lambda}$ を考え，更に強さ $q$ の横磁場を印加した数理模型である．横磁場の為に温度のみの時とは異なる種の相転移が起こる．また，$d$ 次元量子Ising模型は空間に時間と呼ばれる別の座標軸を加えた時空間を考えることによって，$d+1$ 次元の特殊な古典Ising模型と等価であることが知られている．本講演では量子Ising模型に対するレース展開を導出する試みの一端として，古典Ising模型 ($q=0$ の場合の量子Ising模型) に対する新しいレース展開の導出方法を解説する．それ自体はランダムカレント表現を用いて [Sakai (2007) \textit{Commun. Math. Phys.}] [Sakai (2022) \textit{Commun. Math. Phys.}] で既に得られている．ランダムカレント表現は簡単に言えばスピンの言葉をボンドの言葉に翻訳する手法の一種である．本講演では，量子Ising模型で使われる，時空間でのランダムカレント表現 [Bj\"{o}rnberg and Grimmett (2009) \textit{J. Stat. Phys.}] [Crawford and Ioffe (2010) \textit{Commun. Math. Phys.}] を用いる点が先行研究と異なる．横磁場有り ($q > 0$) の場合の研究は現在進行中である．時間に余裕があれば，その現状についても言及する．本研究は坂井哲（北海道大学）との共同研究である．
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Derivation of a lace expansion for the Ising model by a random current representation on space-time [招待講演]
上島芳倫
Random Fields and Processes on Graphs and Fractals 2024年06月口頭発表（一般）京都大学数理解析研究所阿部圭宏;David Croydon;梶野直孝

The lace expansion is one of the powerful tools to investigate critical phenomena. It has succeeded in getting an asymptotic expansion for the critical point for several models, e.g., the self-avoiding walk, ordinary/oriented percolation, the contact process, etc. Our purpose is to obtain such an asymptotic expansion for the quantum Ising model, in which the different type of the phase transition from the classical Ising model is caused by a transverse field, by use of a lace expansion. The lace expansion for the classical Ising model was derived in [Sakai (2007) \textit{Commun. Math. Phys.}], whereas it has not derived for the quantum Ising model yet. In this talk, I show a new derivation of a lace expansion for the classical Ising model, which is the special case of the quantum Ising model without the transverse field. The Hamiltonian in the quantum Ising model are expressed by operators. Thanks to the Lie-Trotter product formula, it is enough to consider the ($d+1$)-dimensional space-time Ising model, which are not given by operator language, instead of the $d$-dimensional Ising model. So far, we have derived a new type of the lace expansion without the transverse field based on the random current representation [Bj\"{o}rnberg and Grimmett (2009) \textit{J. Stat. Phys.}] [Crawford and Ioffe (2010) \textit{Commun. Math. Phys.}] on the space-time. We also expect that this approach helps us to derive a lace expansion in the case that the transverse field is finite. This talk is based on joint work with Akira Sakai (Hokkaido University, Japan).

Derivation of a lace expansion for the Ising model by a random current representation on space-time [招待講演]
上島芳倫
Taiwan Probability Workshop 2024 2024年06月口頭発表（一般）中央研究院數學研究所陳冠宇;陳隆奇;陳定立;何政衞;林偉傑;李志煌

The lace expansion is one of the powerful tools to investigate critical phenomena. It has succeeded in getting an asymptotic expansion for the critical point for several models, e.g., the self-avoiding walk, ordinary/oriented percolation, the contact process, etc. Our purpose is to obtain such an asymptotic expansion for the quantum Ising model, in which the different type of phase transition from the classical Ising model is caused by a transverse field, by use of a lace expansion. The lace expansion for the classical Ising model was derived in [Sakai (2007) \textit{Commun. Math. Phys.}], whereas it has not been derived for the quantum Ising model yet. In this talk, I show a new derivation of a lace expansion for the classical Ising model, which is the special case of the quantum Ising model without the transverse field. The Hamiltonian in the quantum Ising model is expressed by operators. Thanks to the Lie-Trotter product formula, it is enough to consider the ($d+1$)-dimensional space-time Ising model, which is not given by operator language, instead of the $d$-dimensional Ising model. So far, we have derived a new type of lace expansion without the transverse field based on the random current representation [Bj\"{o}rnberg and Grimmett (2009) \textit{J. Stat. Phys.}] [Crawford and Ioffe (2010) \textit{Commun. Math. Phys.}] on the space-time. We also expect that this approach helps us to derive a lace expansion in the case that the transverse field is finite. This talk is based on joint work with Akira Sakai (Hokkaido University, Japan).

Stability of the phase transition and critical behavior of the Ising model against quantum perturbation [招待講演]
上島芳倫
Random Interacting Systems, Scaling Limits, and Universality 2023年12月口頭発表（一般） Institute for Mathematical Sciences National University of Singapore Akira Sakai;Rongfeng Sun

The quantum Ising model is a kind of model of ferromagnetic materials. In this model, spin configurations are regarded as operators but not scalars. Spins are fluctuated by a quantum effect. In the case of the nearest-neighbor setting, Björnberg proved that the (magnetic) susceptibility diverges at the critical inverse temperature and exhibits the power-law behavior on the integer lattice. In particular, its critical exponent takes the mean-field value 1 in dimensions greater than or equal to 4 at finite temperature and in dimensions greater than or equal to 3 at absolute zero. In this talk, I show a lace-expansion approach to prove that the critical behavior for the susceptibility does not change even when the quantum effect is imposed. Physicists believe this conjecture, but we want to give mathematically rigorous proof. So far, we have obtained the differential inequalities for the susceptibility with respect to inverse temperature and derived the lace expansion for the quantum Ising model. They support that the above critical value equals 1. Our derivation of the lace expansion is inspired by the NoBLE, which Fitzner and van der Hofstad derived. This talk is based on joint work with Akira Sakai.
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The stationary density for TASEP-LKF with a closed boundary condition [通常講演]
上島芳倫
2023 NCTS Postdoc Symposium 2023年09月口頭発表（一般）台北市台灣大學次震宇宙館程舜仁;李瑩英

Totally asymptotic simple exclusion processes (TASEP) are one of the models describing traffic flow. We consider the configuration space $\{0, 1\}^\Lambda$, where $\Lambda=\{1, \dots, L\}$ is the path graph with length $L$. It is interpreted that there are cars at each site whose state is $1$ and that there are no cars at each site whose state is $0$. Each car hops to the forward nearest-neighbor site randomly, but two or more cars do not occupy the same site simultaneously (the exclusion rule). In this talk, I will explain TASEP with Langmuir kinetics depending on the occupancy of the forward neighboring site (TASEP-LKF). While TASEP-LKF with the periodic boundary condition is investigated in \cite{isn2016}, I show results for TASEP-LKF with a closed boundary condition. Specifically, I prove that there exists the stationary density uniquely under the mean-field approximation and that the rightmost stationary density is bigger than the second rightmost stationary density. This is based on joint work with Prof. Yuta Arai (Chiba University of Commerce, Japan).

A local limit theorem for the long-range self-avoiding walk [通常講演]
上島芳倫
第32屆南區統計研討會 2023年06月口頭発表（一般）花蓮縣壽豐鄉國立東華大學吳韋瑩

The self-avoiding walk (SAW) is a model added self-avoidance interaction to the random walk. In other words, each path does not visit the same vertex on a graph more than once. It is known that the spread-out short-range SAW enjoys the central limit theorem [van der Hofstad and Slade (2003) AAM]. Taking an average on a ball, they also proved a certain type of a local limit theorem. For the spread-out long-range SAW, the power-law decay of the two-point function was shown in [Chen and Sakai (2019) CMP]. In this talk, I will explain an attempt to prove a local limit theorem for the spread-out long-range SAW in the original sense. Our motivations come from combining the results of the previous researches. This is a joint work with Lung-Chi Chen (National Chengchi University) and Yuki Chino (National Yang Ming Chiao Tung University).
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A local limit theorem for the long-range self-avoiding walk [通常講演]
上島芳倫
2023 NCTS Spring Day 2023年03月口頭発表（一般）台北市台灣大學次震宇宙館李瑩英

The self-avoiding walk (SAW) is a model added self-avoidance interaction to the random walk. In other words, each path does not visit the same vertex on a graph more than once. It is known that the spread-out short-range SAW enjoys the central limit theorem [van der Hofstad and Slade (2003) AAM]. Taking an average on a ball, they also proved a certain type of a local limit theorem. For the spread-out long-range SAW, the power-law decay of the two-point function was shown in [Chen and Sakai (2019) CMP]. In this talk, I will explain an attempt to prove a local limit theorem for the spread-out long-range SAW in the original sense. Our motivations come from combining the results of the previous researches. This is a joint work with Lung-Chi Chen (National Chengchi University) and Yuki Chino (National Yang Ming Chiao Tung University).

閉境界条件でのTASEP-LKFに対するdensity profileについて [通常講演]
上島芳倫
無限粒子系、確率場の諸問題XVII 2023年01月口頭発表（一般）奈良県奈良市奈良女子大学篠田正人;村井浄信;竹居正登;嶽村智子

長距離相互作用を持つ自己回避歩行に対する局所極限定理について [招待講演]
上島芳倫
大規模相互作用系の確率解析 2022年12月口頭発表（一般）福岡市九州大学西新プラザ福島竜輝;永幡幸生;長田博文;角田謙吉

Mean-field behavior for ordinary/oriented bond percolation [通常講演]
上島芳倫
Taipei Postdoc Seminar 2022年11月口頭発表（一般）台北市台灣大學次震宇宙館陳世昕;王賜聖

Percolation is a stochastic model of wetting of porous medium, the spread of blight in an orchard, a forest fire, etc. Specifically, bond percolation is defined by giving the occupied and vacant states $p D(y - x)$ and $1 - p D(y - x)$, respectively, for each edge $\{x, y\}$ on a graph. It is known that phase transitions occur at a critical point $p_\mathrm{c}$ in this model, and it is believed that some quantities exhibit power-law (critical phenomena). For example, it is predicted that the susceptibility (the mean cluster size) $\chi_p$ asymptotically behaves like $(p_\mathrm{c} - p)^{-\gamma}$. The exponent $\gamma$ particularly takes the value $1$ in high dimension, which is called a mean-field value. In this talk, I explain the basic topics of mean-field behavior for percolation models. I also mention the infrared bound and the lace expansion. They are key topics in my research.
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Mean-field behavior for the quantum Ising model [招待講演]
上島芳倫
2022 機率薪傅研討會 2022年11月口頭発表（一般）台北市台灣大學次震宇宙館洪芷漪;劉聚仁

The quantum Ising model is a kind of model of ferromagnetic materials. In this model, we consider spin configurations regarded as operators but not scalars. Due to this, spins are fluctuated by a quantum effect $q\geq 0$. When $q=0$, the model is particularly called the classical Ising model. In the case of the classical one for the nearest-neighbor setting, it is known that the (magnetic) susceptibility $\chi(\beta, 0)$ diverges at the critical inverse temperature $\beta_\mathrm{c}$ and exhibits the power-law behavior on $\mathbb{Z}^d$. In particular, its critical exponent $\gamma$ takes the mean-field value $1$ in $d\geq 4$. In this talk, I show some attempts to prove that the critical behavior for the susceptibility does not change even when the quantum effect is imposed. Physicists believe this conjecture, but we want to give mathematically rigorous proof. So far, we have obtained the differential inequalities for $\chi(\beta, q)$ with respect to $\beta$. They support that $\gamma=1$ with an assumption. Also, I mention attempts to derive the lace expansion, which implies the assumption for the differential inequalities. This talk is based on joint work with Akira Sakai (Hokkaido University, Japan).
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量子Ising模型に対する平均場臨界現象 [招待講演]
上島芳倫
東北大学確率論セミナー 2022年11月口頭発表（一般）宮城県仙台市青葉区東北大学阿部圭宏

The quantum Ising model is a kind of model of ferromagnetic materials. In this model, we consider spin configurations regarded as operators but not scalars. Due to this, spins are fluctuated by a quantum effect $q\geq 0$. When $q=0$, the model is particularly called the classical Ising model. In the case of the classical one for the nearest-neighbor setting, it is known that the (magnetic) susceptibility $\chi(\beta, 0)$ diverges at the critical inverse temperature $\beta_\mathrm{c}$ and exhibits the power-law behavior on $\mathbb{Z}^d$. In particular, its critical exponent $\gamma$ takes the mean-field value $1$ in $d\geq 4$. In this talk, I show some attempts to prove that the critical behavior for the susceptibility does not change even when the quantum effect is imposed. Physicists believe this conjecture, but we want to give mathematically rigorous proof. So far, we have obtained the differential inequalities for $\chi(\beta, q)$ with respect to $\beta$. They support that $\gamma=1$ with an assumption. Also, I mention attempts to derive the lace expansion, which implies the assumption for the differential inequalities. This talk is based on joint work with Akira Sakai (Hokkaido University, Japan).

最近接有向パーコレーションに対するレース展開 [通常講演]
上島芳倫
第18回数学総合若手研究集会〜数学の交叉点〜 2022年03月ポスター発表北海道札幌市北海道大学祐川翼;石井宙志;工藤勇;関元樹;長谷川蒼;波多野幸平;安孫子啓介;田嶌優;藤江克徳;牧田慎平

有向パーコレーションは伝染病の生存・死滅を記述するモデルである．数学的には，格子グラフ $\mathbb{L}^d$ と非負整数全体 $\mathbb{Z}_+$ の直積 $\mathbb{L}^d\times\mathbb{Z}_+$ の辺集合に対して，開・閉なる状態をランダムに与えることで定義される．開の辺で繋がった頂点数の期待値には冪乗則 $(p_\mathrm{c} - p)^{-\gamma}$ が予想されており，特に $d>4$ ならば $\gamma=1$ だと信じられている．講演者らはこれを単純立方格子では $d+1=184$ で，体心立方格子では $d+1=10$ で証明したので，それを紹介する．
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最近接有効パーコレーションに対するレース展開 [通常講演]
上島芳倫
無限粒子系、確率場の諸問題XVI 2021年10月口頭発表（一般）オンライン (Zoom) 篠田正人;村井浄信;竹居正登;嶽村智子
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最近接有向パーコレーションに対するレース展開 [通常講演]
上島芳倫
確率論若手セミナー・オンライン 2020年09月口頭発表（一般）オンライン (Zoom) 中島誠

体心立方格子上の最近接無向・有向パーコレーションに対するレース展開の解析 [招待講演]
上島芳倫
関西確率論セミナー 2019年12月口頭発表（一般）京都府京都市京都大学楠岡誠一郎

The lace expansion is a powerful tool to analyze the critical behavior in high dimension. It is applied to various stochastic models, such as self-avoiding walk, percolation, Ising model etc. It is conjectured that the nearest-neighbor ordinary and oriented percolations exhibit the mean-field behavior in dimension $d$ above the upper critical dimension $d_\mathrm{c}=6, 4$, respectively, so that we want to prove them by the lace expansions. To achieve this, we consider the $d$-dimensional body-centered cubic (BCC) lattice. In this talk, I will show current statuses of the above problems. The research on the ordinary percolation is based on a joint works with Satoshi Handa (Fujitsu Laboratories Ltd.) and Akira Sakai (Hokkaido University, Japan). That on the oriented percolation is based on a joint work with Satoshi Handa (id.) and Lung-Chi Chen (National Chengchi University, Taiwan).

量子Ising模型の確率幾何的表現について [招待講演]
上島芳倫
大規模相互作用の確率解析 2019年11月口頭発表（一般）大阪府豊中市大阪大学福島竜輝;舟木直久;永幡幸生;長田博文;角田謙吉

We will consider a critical behavior of the susceptibility $\chi(\beta)$ with respect to the inverse temperature $\beta$ for the quantum Ising ferromagnet. As a first step, we followed the established way for the classical Ising model [M.~Aizenman, \emph{Commun. Math. Phys.} \textbf{86}, 1982] and derived an inequalities for $\chi(\beta)$ via the Suzuki-Trotter transformation (see, e.g., [K., RIMS K\^{o}ky\^{u}roku \textbf{2116}, 2019] or [S. Handa, Ph.D. thesis, 2019]). At that time, however, we had used the monotonicity for $\chi(\beta)$ with respect to $\beta$ with an extra condition. Our next aim is to drop such condition and show the infrared bound for the quantum Ising model. In this talk, I will show some attempts to prove the critical behavior via another way: the graphical representation in terms of the space-time Ising model which originates from [J.E.~Bj\"{o}rnberg and G.R.~Grimmett, \textit{J. Stat. Phys.}~\textbf{136}, 2009]. This is based on a joint work with Satoshi Handa (Fujitsu Laboratories Ltd.) and Akira Sakai (Hokkaido University).

確率セル・オートマトンによる最適解の探索 [通常講演]
上島芳倫
日本数学会2019年度秋季総合分科会 2019年09月口頭発表（一般）石川県金沢市金沢大学日本数学会

確率セル・オートマトンによるIsing 模型の基底状態探索への試み [通常講演]
上島芳倫
確率論ヤングサマーセミナー 2019年08月口頭発表（一般）宮城県刈田郡蔵王町遠刈田温泉さんさ亭永沼伸顕

量子Ising 模型における平均場臨界現象 [通常講演]
上島芳倫
第12回日本数学会季期研究所「確率解析、確率場と可積分確率」 2019年08月ポスター発表福岡市九州大学伊都キャンパス江崎翔太;針谷祐;星野壮登;稲濱譲;篠田正人;白井朋之

確率幾何的表現を用いた量子Ising模型の高次元臨界現象の解析 [通常講演]
上島芳倫
新潟確率論ワークショップ 2019年03月口頭発表（一般）新潟市新潟大学駅南キャンパスときめいと永幡幸生

量子Ising 模型における平均場臨界現象 [通常講演]
上島芳倫
第15回数学総合若手研究集会 2019年03月口頭発表（一般）北海道札幌市北海道大学福田一貴;青木雅允;植田優基;上島芳倫;矢不俊文;新村貴之;佐藤直飛;豊川永喜;松坂公暉;山形颯;吉田啓佑

本研究は坂井准教授（北大）と半田氏（北大）との共同研究である．量子Ising模型は古典Ising模型のスピンを作用素で置換し横磁場を印加したモデルである．これは温度を固定し相互作用係数と横磁場を変化させたとき，高次元で平均場臨界現象を示すことが知られている．一方で，講演者らは相互作用係数と横磁場を固定し温度を変化させたときの振舞に興味がある．本講演ではこの問題について現在までに得られた結果を紹介する．

確率幾何的表現を用いた量子Ising 模型の平均場臨界現象の解析 [通常講演]
上島芳倫
確率論シンポジウム 2018年12月口頭発表（一般）京都府京都市京都大学会田茂樹;久保田直樹;熊谷隆;佐々田槙子;白石大典

体心立方格子上の最近接モデルに対するレース展開 [通常講演]
上島芳倫
第14回数学総合若手研究集会 2018年ポスター発表北海道札幌市北海道大学半田悟;小森大地;藤沢好;Albert Rodríguez Mulet;青木雅允;上島芳倫;福田一貴;矢不俊文

The lace expansion for the nearest-neighbor models on the BCC lattice [通常講演]
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Recent Progress in Probability Theory and Its Applications 2017年07月口頭発表（一般）北海道札幌市北海道大学坂井哲

The lace expansion for the nearest-neighbor models on the BCC lattice [通常講演]
上島芳倫
Short talk in PIMS-CRM Summer School in Probability 2017年06月口頭発表（一般）バンクーバーブリティッシュ・コロンビア大学 Omer Angel;Mathav Murugan;Edwin Perkins;Gordon Slade

体心立方格子上の最近接自己回避歩行に対するレース展開 [通常講演]
上島芳倫
第13回数学総合若手研究集会 2017年02月ポスター発表北海道札幌市北海道大学中村文彦;相川勇輔;浅原啓輔;阿部眞尊;小森大地;齋藤逸人;半田悟;藤沢好;本多俊一;Albert Rodríguez Mulet

体心立方格子上の最近接モデルに対するレース展開 [通常講演]
上島芳倫
確率論シンポジウム 2016年12月口頭発表（一般）京都府京都市京都大学中島誠;福島竜輝;福山克司;矢野孝次;矢野裕子

The lace expansion for the self-avoiding walk on the BCC lattice [通常講演]
上島芳倫
Pisa-Hokkaido Summer School on Mathematics and its Applications 2016年09月ポスター発表ピサピサ大学 Hideo Kubo;Luigi Marengo;Mario Salvetti;Hiroaki Terao