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作者：Chen, Hongyi; Ouyang, Cheng
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
摘要：On a closed Riemannian manifold, we construct a family of intrinsic Gaussian noises indexed by a regularity parameter alpha >= 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \ge 0$$\end{document} to study the well-posedness of the parabolic Anderson model. We show that with rough initial conditions, the eq...
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作者：Calka, Pierre; Demichel, Yann
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper, we consider a regular tessellation of the Euclidean plane and the sequence of its geometric scalings by negative powers of a fixed integer. We generate iteratively random sets as the union of adjacent tiles from these rescaled tessellations. We encode this geometric construction into a combinatorial object, namely a multitype Galton-Watson tree. Our main result concerns the geometric properties of the limiting planar set. In particular, we show that both box and Hausdorff dimens...
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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：Aistleitner, Christoph; Fruhwirth, Lorenz; Hauke, Manuel; Manskova, Maryna
作者单位：Graz University of Technology; University of Passau; Norwegian University of Science & Technology (NTNU)
摘要：In a recent paper, Aistleitner, Gantert, Kabluchko, Prochno and Ramanan studied large deviation principles (LDPs) for lacunary trigonometric sums Sigma(N)(K=1 )cos(2 pi n(k)x), where the sequence (n(k)) k >= 1 satisfies the Hadamard gap condition n(k+1)/nk >= q >1 for k >= 1. A crucial ingredient in their work were asymptotic estimates for the moment generating function (MGF) of such sums, which turned out to depend on the fine arithmetic structure of the sequence (n(k)) k >= 1 in an intricate...
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作者：Benaim, Michel; Tough, Oliver
作者单位：University of Neuchatel; University of Bath
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作者：Ding, Jian; Yang, Peng; Zhuang, Zijie
作者单位：Peking University; University of Pennsylvania
摘要：In this paper, we study the evolution of the zero-temperature random field Ising model as the mean of the external field M increases from -infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\infty $$\end{document} to infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{a...
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作者：Chaintron, Louis-Pierre; Conforti, Giovanni
作者单位：Universite PSL; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure (ENS); Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; University of Padua
摘要：We consider a system of diffusion processes interacting through their empirical distribution. Assuming that the empirical average of a given observable can be observed at any time, we derive regularity and quantitative stability results for the optimal solutions in the associated version of the Gibbs conditioning principle. The proofs rely on the analysis of a McKean-Vlasov control problem with distributional constraints. Some new estimates are derived for Hamilton-Jacobi-Bellman equations and...
