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作者：Duminil-Copin, Hugo; Panis, Romain
作者单位：Universite Paris Saclay; University of Geneva
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作者：Jain, Vishesh; Sawhney, Mehtaab
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Columbia University
摘要：Consider shuffling a deck of n cards, labeled 1 through n, as follows: at each time step, pick one card uniformly with your right hand and another card, independently and uniformly with your left hand; then swap the cards. How long does it take until the deck is close to random? Diaconis and Shahshahani showed that this process undergoes cutoff in total variation distance at time t=& LeftFloor;(nlogn)/2 & RightFloor;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepa...
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作者：Chen, Yilin; Fehrman, Benjamin; Xu, Weijun
作者单位：Peking University; Louisiana State University System; Louisiana State University; Westlake University
摘要：We consider the periodic homogenisation problem for the generalised parabolic Anderson model on the two dimensional torus. We show that, for the renormalisation that respects Wick ordering, the homogenisation and renormalisation procedures commute. The main novelty is to identify a suitable solution ansatz beyond the usual para-controlled ansatz to set up a fixed point problem uniform in the homogenisation parameter. After that, one further utilises cancellations and resonances from the homoge...
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作者：Donderwinkel, Serte; Khanfir, Robin
作者单位：University of Groningen; University of Groningen; McGill University
摘要：We obtain assumption-free, non-asymptotic, uniform bounds on the product of the height and the width of uniformly random trees with a given degree sequence, conditioned Bienaym & eacute; trees and simply generated trees. We show that for a tree of size n, this product is O(nlogn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin...
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作者：He, Yukun; Huang, Jiaoyang; Wang, Chen
作者单位：Fudan University; University of Pennsylvania; City University of Hong Kong
摘要：We consider a class of sparse random matrices, which includes the adjacency matrix of the Erd & odblac;s-R & eacute;nyi graph G(N,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textbf{G}(N,p)$$\end{document}. For N-1+o(1)<= p <= 1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepack...
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作者：Hip, Andres A. Contreras; Gwynne, Ewain
作者单位：University of Chicago
摘要：We investigate the notion of curvature in the context of Liouville quantum gravity (LQG) surfaces. We define the Gaussian curvature for LQG, which we conjecture is the scaling limit of discrete curvature on random planar maps. Motivated by this, we study asymptotics for the discrete curvature of & varepsilon;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength...
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作者：Duminil-Copin, Hugo; Panis, Romain
作者单位：Universite Paris Saclay; University of Geneva
摘要：This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions d > 4. Among other results, we obtain up-to-constant estimates for the full-space and half-space two-point functions in the critical and near-critical regimes. A companion paper proposes a similar analysis for spread-out Bernoulli percolation in dimensions d > 6 [10].
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作者：Hou, Haojie; Zhang, Xicheng
作者单位：Nankai University; Beijing Institute of Technology; Shenzhen MSU-BIT University
摘要：We use probabilistic techniques to derive sharp and explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator where Delta v alpha/2 denotes the fractional Laplacian acting on the velocity variable v . We also establish logarithmic gradient estimates with respect to both the spatial variable x and the velocity variable v . In fact, our estimates are obtained for more general nonsymmetric stable-like operators and make the dependence on the lower and upper bounds of the k...
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作者：Avraham-Re'em, Nachi; Roy, Emmanuel
作者单位：Technion Israel Institute of Technology; Universite Paris 13
摘要：We prove that for an arbitrary indexing group, every ergodic infinitely divisible stationary process that is separable in probability is weakly mixing. This shows that, as in the well-known case of Gaussian stationary processes, ergodicity implies weak mixing is intrinsic to infinite divisibility, removing all structural assumptions on the group from prior results. The main ingredient is a general construction of stochastically continuous extensions for separable in probability stationary proc...
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作者：Arizmendi, Octavio; Hasebe, Takahiro; Kitagawa, Yu
作者单位：Hokkaido University; Kyoto University
