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作者：Johnston, Tom; Kronenberg, Gal; Roberts, Alexander; Scott, Alex
作者单位：University of Bristol; University of Oxford
摘要：In the graph shotgun assembly problem, we are given the balls of radius r around each vertex of a graph and asked to reconstruct the graph. We study the shotgun assembly of the Erd & odblac;s-R & eacute;nyi random 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}$${\mathcal {G}}(n,p)$$\end{document} for a ...
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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：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 ...
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作者：Bauerschmidt, Roland; Bodineau, Thierry; Dagallier, Benoit
作者单位：New York University; Centre National de la Recherche Scientifique (CNRS)
摘要：Glauber dynamics of the Ising model on a random regular graph is known to mix fast below the tree uniqueness threshold and exponentially slowly above it. We show that Kawasaki dynamics of the canonical ferromagnetic Ising model on a random d-regular graph mixes fast beyond the tree uniqueness threshold when d is large enough (and conjecture that it mixes fast up to the tree reconstruction threshold for all d >= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackag...
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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：Jirak, Moritz; Minsker, Stanislav; Shen, Yiqiu; Wahl, Martin
作者单位：University of Vienna; University of Southern California; University of Southern California; University of Bielefeld
摘要：We prove Fuk-Nagaev and Rosenthal-type inequalities for sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only low orders. Our bounds depend on the intrinsic dimensional characteristics such as the effective rank, as opposed to the dimension of the ambient space. We illustrate the advantages of such results through several applications, including new moment inequalities for sample covariance matrices and their eigenvectors w...
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作者：Archer, Eleanor; Hartarsky, Ivailo; Kolesnik, Brett; Olesker-Taylor, Sam; Schapira, Bruno; Valesin, Daniel
作者单位：Technische Universitat Wien; University of Warwick; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In Catalan percolation, all nearest-neighbour edges {i, i + 1} along Z are initially occupied, and all other edges are open independently with probability p. Open edges {i, j} are occupied if some pair of edges {i, k} and {k, j}, with i < k < j, become occupied. This model was introduced by Gravner and the third author, in the context of polluted graph bootstrap percolation. We prove that the critical pc is strictly between that of oriented site percolation on Z(2) and the Catalan growth rate ...
