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作者：He, Yukun
作者单位：Fudan University
摘要：Let A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document} be the adjacency matrix of the Erd & odblac;s-R & eacute;nyi directed graph G(N,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mat...
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作者：Adhikari, Arka; Park, Jiyun
作者单位：University System of Maryland; University of Maryland College Park; Stanford University
摘要：We prove a moderate deviation principle for the capacity of the range of random walk in Z5 . Depending on the scale of deviation, we get two different regimes. We observe Gaussian tails when the deviation scale is smaller than n1/2(logn)3/4 . Otherwise, we get non-Gaussian tails with a constant arising from a generalized Gagliardo-Nirenberg inequality. This is analogous to the behavior of the volume of the random walk range in Z3 . Our methods can also be applied to the d=4 case to prove the m...
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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：Lemoine, Thibaut
作者单位：Universite PSL; College de France
摘要：We derive new formulas for the expectation and variance of Wilson loops for any contractible simple loop on a compact orientable surface of genus 1 and higher, in the model of two-dimensional Yang-Mills theory with structure group U(N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm U}(N)$$\end{document}. T...
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作者：Kremp, Helena; Perkowski, Nicolas
作者单位：Technische Universitat Wien; Free University of Berlin
摘要：We introduce a weak solution concept (called rough weak solutions) for singular SDEs with additive alpha-stable L & eacute;vy noise (including the Brownian noise case) and prove its well-posedness and equivalence to martingale solutions from Kremp and Perkowski (Bernoulli 28(3):1757-1783, 2022. https://doi.org/10.3150/21-BEJ1394) in Young and rough regularity regimes. In the rough regime this requires to construct certain rough integrals with the help of the stochastic sewing lemma, which we u...
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作者：Eckstein, Stephan
作者单位：Eberhard Karls University of Tubingen
摘要：Motivated by the entropic optimal transport problem in unbounded settings, we study versions of Hilbert's projective metric for spaces of integrable functions of bounded growth. These versions of Hilbert's metric originate from cones which are relaxations of the cone of all non-negative functions, in the sense that they include all functions having non-negative integral values when multiplied with certain test functions. We show that kernel integral operators are contractions with respect to s...
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作者：Gess, Benjamin; Gvalani, Rishabh S.; Konarovskyi, Vitalii
作者单位：Technical University of Berlin; Max Planck Society; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Hamburg; National Academy of Sciences Ukraine; Institute of Mathematics of NASU
摘要：The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optimal rate of convergence. As a second main result, a quantitative central limit theorem for such SPDEs is derived, again, with optimal rate of convergence. The results apply, in particular, to the convergence in the mean-field scaling of stochastic gradient descent dynamics in overparametrized, shallow neural networks ...
