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math.PR2024
Graphical proof of Ginibre's inequality
Yuki Tokushige
In this short note, we will give a new combinatorial proof of Ginibre's inequality for XY models. Our proof is based on multigraph representations introduced by van Engelenburg-Lis…
math.PR2024
Scaling limits for random walks on long range percolation clusters
Noam Berger, Yuki Tokushige
We study limit laws for simple random walks on supercritical long-range percolation clusters on the integer lattice. For the long range percolation model, the probability that two…
math.PR2019
Differentiability of the speed of biased random walks on Galton-Watson trees
Adam Bowditch, Yuki Tokushige
We prove that the speed of a -biased random walk on a supercritical Galton-Watson tree is differentiable for such that the walk is ballistic and obeys a central limit theore…