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作者：Hutchcroft, Tom
作者单位：California Institute of Technology
摘要：In long-range percolation on Z(d), we connect each pair of distinct points x and y by an edge independently at random with probability 1-exp(-beta parallel to x-y parallel to(-d-alpha)), where alpha> 0 is fixed and beta >= 0 is a parameter. In a previous paper, we proved that if 0 < alpha < d then the critical two-point function satisfies the spatially averaged upper bound 1/ r(d) & sum;(d)( x is an element of[-r,r]) (P)beta(c)(0 <-> x) <= r(-d+alpha) for every r >= 1. This upper bound is beli...
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作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Bonn; Imperial College London; University of Cambridge
摘要：We investigate the bond percolation model on transient weighted graphs G induced by the excursion sets of the Gaussian free field on the corresponding metric graph. Under the sole assumption that its sign clusters do not percolate, we derive an extension of Lupu's formula for the two-point function at criticality. We then focus on the low-dimensional case 0 < nu < (alpha)/(2) , where alpha governs the polynomial volume growth of G and nu the decay rate of the Green's function on G. In particul...
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作者：Hutchcroft, Tom
作者单位：California Institute of Technology
摘要：In long-range percolation on Z(d), we connect each pair of distinct points x and y by an edge independently at random with probability 1-exp(-beta parallel to x-y parallel to(-d-alpha)), where alpha> 0 is fixed and beta >= 0 is a parameter. In a previous paper, we proved that if 0 < alpha < d then the critical two-point function satisfies the spatially averaged upper bound 1/ r(d) & sum;(d)( x is an element of[-r,r]) (P)beta(c)(0 <-> x) <= r(-d+alpha) for every r >= 1. This upper bound is beli...
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作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Bonn; Imperial College London; University of Cambridge
摘要：We investigate the bond percolation model on transient weighted graphs G induced by the excursion sets of the Gaussian free field on the corresponding metric graph. Under the sole assumption that its sign clusters do not percolate, we derive an extension of Lupu's formula for the two-point function at criticality. We then focus on the low-dimensional case 0 < nu < (alpha)/(2) , where alpha governs the polynomial volume growth of G and nu the decay rate of the Green's function on G. In particul...
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作者：Chu, Raymond; Kim, Inwon; Kim, Young-Heon; Nam, Kyeongsik
作者单位：University of California System; University of California Los Angeles; University of British Columbia; Korea Advanced Institute of Science & Technology (KAIST)
摘要：We study the nonlocal Stefan problem, where the phase transition is described by a nonlocal diffusion as well as the change of enthalpy functions. By using a stochastic optimization approach introduced in Kim and Kim (The Stefan problem and free targets of optimal Brownian martingale transport, 2021. arXiv preprint arXiv:2110.03831), we construct global-time weak solutions and give a probabilistic interpretation for the solutions. An important ingredient in our analysis is a probabilistic inte...
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作者：Dembin, Barbara; Severo, Franco
作者单位：Universites de Strasbourg Etablissements Associes; Centre National de la Recherche Scientifique (CNRS); Universite de Strasbourg; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Jean Monnet; Universite Lyon 1; Ecole Centrale de Lyon; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove that the supercritical phase of Voronoi percolation on R-d, d >= 3, is well behaved in the sense that for every p>p(c)(d) local uniqueness of macroscopic clusters happens with high probability. As a consequence, truncated connection probabilities decay exponentially fast and percolation happens on sufficiently thick 2D slabs. This is the analogue of the celebrated result of Grimmett and Marstrand for Bernoulli percolation and serves as the starting point for renormalization techniques...
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作者：Menshikov, Mikhail; Popov, Serguei; Wade, Andrew
作者单位：Durham University; Universidade do Porto
摘要：We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which suppresses jumps that would lead to more than one particle occupying any site. Under appropriate hypotheses on the jump rates (uniformly bounded rates is sufficient) and started from an initial condition that is a finite perturbation of the close-packed ...
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作者：Biskup, Marek
作者单位：University of California System; University of California Los Angeles
摘要：We study the asymptotic distribution of random walks on Zd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb Z<^>d$$\end{document} (d >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgr...
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作者：Gu, Haotian; Zhang, Zhenyuan
作者单位：University of California System; University of California Los Angeles; Stanford University
摘要：We investigate the low moments E[|A(N) |(2q)], 0 < q <= 1 of secular coefficients A(N) of the critical non-Gaussian holomorphic multiplicative chaos, i.e. coefficients of zN in the power series expansion of exp(Sigma(infinity)(k = 1) X-k z(k)/ root k), where {X-k} (k >= 1) are i.i.d. rotationally invariant unit variance complex random variables. Inspired by Harper's remarkable result on random multiplicative functions, Soundararajan and Zaman recently showed that if each X-k is standard comple...
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作者：Qin, Shuo
摘要：Under suitable moment assumptions, we show that a genuinely d-dimensional step-reinforced random walk undergoes a phase transition between recurrence and transience in dimensions d=1,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=1,2$$\end{document}, and that it is transient for all reinforcement parameters in ...
