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Mercoledì 27 Maggio alle ore 13.00, Yuval Peres (BIMSA Beijing) terrà il seminario di Probabilità e Fisica Matematica dal titolo "Random walk on dynamical percolation: separating critical and supercritical regimes".
Abstract: In Dynamical Percolation each edge is open with probability p, refreshing its status at rate 𝜇 > 0. This process was introduced in the 1990s by Haggstrom, Steif and the speaker, motivated by a question of Malliavin. Remarkable results on exceptional times in two dimensions were obtained by Schramm, Steif, Garban and Pete. We study random walk on dynamical percolation in the lattice ℤ^d, where the walk moves along open edges at rate 1. Let p_c = p_c(d) denote the critical value for static percolation. For p < p_c and 𝜇 < 1, joint work with Stauffer and Steiff (PTRF, 2015) showed the mean squared displacement is of order t𝜇. For p > p_c, we prove that the mean squared displacement is of order t, uniformly in 0 < 𝜇 < 1, refining results obtained with Sousi and Steif (PTRF, 2020). In the critical regime p= p_c, we prove that if d= 2 or d > 10, then the mean squared displacement is at most O(t𝜇^a) where a = a(d) > 0. We will show simulations to illustrate the process. (Joint work with Chenlin Gu, Jianping Jiang, Zhan Shi, Hao Wu and Fan Yang.)
Il seminario si svolgerà in presenza presso il Dipartimento di Matematica e Fisica, Lungotevere Dante, 376 - aula B308.
