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作者：Osada, Hirofumi
作者单位：Chubu University
摘要：We prove that the tagged particles of infinitely many Brownian particles in R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbb {R}} <^>2$$\end{document} interacting via a logarithmic (two-dimensional Coulomb) potential with inverse temperature beta=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepa...
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作者：Barraquand, Guillaume; Corwin, Ivan; Das, Sayan
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite; Sorbonne Universite; Columbia University; University of Chicago
摘要：We consider the point-to-point log-gamma polymer of length 2N in a half-space with i.i.d. Gamma(-1)(2 theta) distributed bulk weights and i.i.d. Gamma(-1)(alpha + theta) distributed boundary weights for theta > 0 and alpha > -theta. We establish the KPZ exponents (1/3 fluctuation and 2/3 transversal) for this model when alpha = N-1/3 mu for mu is an element of R fixed (critical regime) and when alpha > 0 is fixed (supercritical regime). In particular, in these two regimes, we show that after a...
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作者：Mariani, Mauro; Pardoux, Etienne; Velleret, Aurelien
作者单位：HSE University (National Research University Higher School of Economics); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We prove the existence and uniqueness of a quasi-stationary distribution for three stochastic processes derived from the model of Muller's ratchet. This model was invented with the aim of evaluating the limitations of an asexual reproduction mode in preventing the accumulation of deleterious mutations through natural selection alone. The main considered model is non-classical, as it is a stochastic diffusion evolving on an irregular set of infinite dimension with hard killing on a hyperplane. ...
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作者：Alvarado, Jose D.; de Oliveira, Leonardo Goncalves; Griffiths, Simon
作者单位：University of Ljubljana
摘要：We consider the question of determining the probability of triangle count deviations in the Erdos-Renyi random graphs G (n,m) and G (n,p)with densities larger than n(-1/2)(log n)(1/2). In particular, we determine the log probability log P(N-Delta(G) > (1+delta)p(3)n(3))up to a constant factor across essentially the entire range of possible deviations, in both the G (n,m) and G (n,p) model. For the G(n,p) model, we also prove a stronger result, up to a(1+o(1)) factor, in the non-localised regim...
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作者：Favaro, S.; Hanin, B.; Marinucci, D.; Nourdin, I.; Peccati, G.
作者单位：University of Turin; Princeton University; University of Rome Tor Vergata; University of Luxembourg
摘要：We study the distribution of a fully connected neural network with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant n. Under mild assumptions on the non-linearity, we obtain quantitative bounds on normal approximations valid at large but finite n and any fixed network depth. Our theorems show both for the finite-dimensional distributions and the entire process, that the distance between a random fully connected network (and its derivative...
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作者：Shen, Hao; Zhu, Rongchan; Zhu, Xiangchan
作者单位：University of Wisconsin System; University of Wisconsin Madison; Beijing Institute of Technology; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：In this paper we continue the study of large N problems for the Wick renormalized linear sigma model, i.e. N-component Phi 4 model, in two spatial dimensions, using stochastic quantization methods and Dyson-Schwinger equations. We identify the large N limiting lawof a collection ofWick renormalized O(N) invariant observables. In particular, under a suitable scaling, the quadratic observables converge in the large N limit to amean-zero (singular) Gaussian field denoted byQwith an explicit covar...
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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 ...
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作者：Benaim, Michel; Tough, Oliver
作者单位：University of Neuchatel; University of Bath
摘要：We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the Riemannian measure. This is applied to Markov chains obtained by random composition of maps and to piecewise deterministic Markov processes obtained by random switching between flows.
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作者：Benard, Timothee; Breuillard, Emmanuel
作者单位：Centre National de la Recherche Scientifique (CNRS); University of Oxford
摘要：We establish the (non-lattice) local limit theorem for products of i.i.d. random variables on an arbitrary simply connected nilpotent Lie group G, where the variables are allowed to be non-centered. Our result also improves on the known centered case by proving uniformity for two-sided moderate deviations and allowing measures with a moment of order 2(dimG)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \us...
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作者：Du, Hang; Gong, Shuyang; Huang, Rundong
作者单位：Massachusetts Institute of Technology (MIT); Peking University
摘要：We study the graph alignment problem over two independent Erdos-R & eacute;nyi random graphs on n vertices, with edge density p falling into two regimes separated by the critical window around p(c ):= root log n/n. Our result reveals an algorithmic phase transition for this random optimization problem: polynomial-time approximation schemes exist in the sparse regime, while statistical-computational gap emerges in the dense regime. Additionally, we establish a sharp transition on the performanc...
