研究

確率論

相転移を含む確率モデル、不均一な空間上のランダムウォーク

J. Misumi : Critical values in a long-range percolation on spaces like fractals, Journal of Statistical Physics, 125 (2006), 877-887.
J. Misumi : Estimates on the effective resistance in a long-range percolation on Z^d, Journal of Mathematics of Kyoto University, 48 (2008), 389-400.
T. Kumagai and J. Misumi : Heat kernel estimates for strongly recurrent random walk on random media, Journal of Theoretical Probability, 21 (2008), 910-935.
J. Misumi : Heat kernel estimates for random walks on some kinds of one-dimensional continuum percolation clusters, Tokyo Journal of Mathematics, 34 (2011), 1-17.
J. Misumi : Estimates on the effective resistance in anisotropic long-range percolation on Z^2, Statistics and Probability Letters, 83 (2013), 953-959.
J. Misumi : The diameter of a long-range percolation cluster on pre-Sierpinski gasket, Journal of Statistical Physics, 158 (2015), 1083-1089.
J. Misumi : The mixing time of a random walk on a long-range percolation cluster in pre-Sierpinski gasket, Journal of Statistical Physics, 165 (2016), 153-163.
J. Misumi : The diameter of a long-range percolation cluster on generalized pre-Sierpinski carpet and regular tree, Journal of Statistical Physics, 174 (2019), 276-286.

J. Misumi : Transience and recurrence for random walks on anisotropic long-range percolation clusters in Z^2, preprint.
三角淳 : Long-range percolation入門, 第３回生物数学の理論とその応用, 数理解析研究所講究録, 1551 (2007), 75-80.
三角淳 : Sierpinski gasket格子上の長距離浸透モデルにおけるランダムウォークの混合時間と等周定数, 確率論シンポジウム, 数理解析研究所講究録, 2116 (2019), 33-38.