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M. Jara, C. Landim, K. Tsunoda, Derivation of viscous Burgers equations from weakly asymmetric exclusion processes, *Annales de l'Institut Henri Poincaré, Probabilités et Statistiques*, 10.1214/20-aihp1075, 57, 1, 169-194, 2021.02. |

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Tadahisa Funaki, Kenkichi Tsunoda, Motion by Mean Curvature from Glauber-Kawasaki Dynamics, *JOURNAL OF STATISTICAL PHYSICS*, 10.1007/s10955-019-02364-7, 177, 2, 183-208, 2019.10, We study the hydrodynamic scaling limit for the Glauber-Kawasaki dynamics. It is known that, if the Kawasaki part is speeded up in a diffusive space-time scaling, one can derive the Allen-Cahn equation which is a kind of the reaction-diffusion equation in the limit. This paper concerns the scaling that the Glauber part, which governs the creation and annihilation of particles, is also speeded up but slower than the Kawasaki part. Under such scaling, we derive directly from the particle system the motion by mean curvature for the interfaces separating sparse and dense regions of particles as a combination of the hydrodynamic and sharp interface limits.. |

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Akshay Goel, Khanh Duy Trinh, Kenkichi Tsunoda, Strong Law of Large Numbers for Betti Numbers in the Thermodynamic Regime, *JOURNAL OF STATISTICAL PHYSICS*, 10.1007/s10955-018-2201-z, 174, 4, 865-892, 2019.02, We establish the strong law of large numbers for Betti numbers of random ech complexes built on RN-valued binomial point processes and related Poisson point processes in the thermodynamic regime. Here we consider both the case where the underlying distribution of the point processes is absolutely continuous with respect to the Lebesgue measure on RN and the case where it is supported on a C1 compact manifold of dimension strictly less than N. The strong law is proved under very mild assumption which only requires that the common probability density function belongs to Lp spaces, for all 1p<.. id="gencho_ronbuns10210502" class="qir_handle_link"> |

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Yasuaki Hiraoka, Kenkichi Tsunoda, Limit Theorems for Random Cubical Homology, *DISCRETE & COMPUTATIONAL GEOMETRY*, 10.1007/s00454-018-0007-z, 60, 3, 665-687, 2018.10, This paper studies random cubical sets in R-d. Given a cubical set X. R-d, a random variable.Q. [0, 1] is assigned for each elementary cube Q in X, and a random cubical set X(t) is defined by the sublevel set of X consisting of elementary cubes with.Q |

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Kenkichi Tsunoda, Hydrodynamic limit for a certain class of two-species zero-range processes, *JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN*, 10.2969/jmsj/06820885, 68, 2, 885-898, 2016.04, Grosskinsky and Spohn [5] studied several-species zero-range processes and gave a necessary and sufficient condition for translation invariant measures to be invariant under such processes. Based on this result, they investigated the hydrodynamic limit. In this paper, we consider a certain class of two-species zero-range processes which are outside of the family treated by Grosskinsky and Spohn. We prove a homogenization property for a tagged particle and apply it to derive the hydrodynamic limit under the diffusive scaling.. |

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C. Landim, R. Misturini, K. Tsunoda, Metastability of Reversible Random Walks in Potential Fields, *JOURNAL OF STATISTICAL PHYSICS*, 10.1007/s10955-015-1298-6, 160, 6, 1449-1482, 2015.09, Let Xi be an open and bounded subset of , and let F ; Xi -> R be a twice continuously differentiable function. Denote by the discretization of Xi, Xi(N) = Xi boolean AND and denote by the continuous-time, nearest-neighbor, random walk on which jumps from to at rate . We examine in this article the metastable behavior of among the wells of the potential F.. |

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K. Tsunoda, Derivation of a free boundary problem from an exclusion process with speed change, *Markov Processes Relat. Fields*, 21, 263-273, 2015.01. |