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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：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：Li, Xinyi; Shiraishi, Daisuke
作者单位：Peking University; Kyoto University
摘要：In this work we consider loop-erased random walk (LERW) and its scaling limit in three dimensions, and prove that 3D LERW parametrized by renormalized length converges to its scaling limit parametrized by some suitable measure with respect to the uniform convergence topology in the lattice size scaling limit. Our result greatly improves the work (Kozma in Acta Math 199:29-152, 2007) of Gady Kozma which establishes the weak convergence of the rescaled trace of 3D LERW towards a random compact s...
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作者：Callegaro, Alice; Roberts, Matthew I.
作者单位：Technical University of Munich; University of Bath
摘要：We define a fragmentation process which involves rectangles breaking up into progressively smaller pieces at rates that depend on their shape. Long, thin rectangles are more likely to break quickly, whereas squares break more slowly. Each rectangle is also more likely to split along its longest side. We are interested in how the system evolves over time: how many fragments are there of different shapes and sizes, and how did they reach that state? Using a standard transformation this fragmenta...
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作者：Jiao, Yong; Osekowski, Adam; Wu, Lian
作者单位：Central South University; University of Warsaw
摘要：We introduce the notion of differential subordination in the context of noncommutative continuous-time martingales and show that for 2 < infinity this domination enforces the corresponding L-p bound between the two processes. As applications, we obtain best-order L-p inequalities for the second-order Riesz transforms on a class of group von Neumann algebras equipped with a conditionally negative length function. The proof relies on a novel stochastic representation of these second-order operat...
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作者：Scardia, Lucia; Zemas, Konstantinos; Zeppieri, Caterina Ida
作者单位：Heriot Watt University; University of Bonn; University of Munster
摘要：In this paper we study the convergence of nonlinear Dirichlet problems for systems of variational elliptic PDEs defined on randomly perforated domains of R-n. Under the assumption that the perforations are small balls whose centres and radii are generated by a stationary short-range marked point process, we obtain in the critical-scaling limit an averaged nonlinear analogue of the extra term obtained in the classical work of Cioranescu and Murat (Res Notes Math III, 1982). In analogy to the ra...
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作者：Kohler-Schindler, Laurin; Lehmkuehler, Matthis
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider a critical Fortuin-Kasteleyn (FK) percolation with cluster weight q is an element of[1,4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q \in [1,4)$$\end{document} in the plane, and color its clusters in red (respectively blue) with probability r is an element of(0,1)\documentclass[12pt]{minimal} \usep...
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作者：Bao, Zhigang; Lee, Jaehun; Xu, Xiaocong
作者单位：Hong Kong University of Science & Technology
摘要：In this paper, we study the smallest non-zero eigenvalue of the sample covariance matrices S(Y) = YY *, where Y = ( yi j) is an M x N matrix with iid mean 0 variance N -1 entries. We consider the regime M = M(N) and M/ N. c8. R\{1} as N. 8. It is known that for the extreme eigenvalues of Wigner matrices and the largest eigenvalue of S(Y), a weak 4thmoment condition is necessary and sufficient for the Tracy-Widom law (Ding and Yang in Ann Appl Probab 28(3):1679-1738, 2018. https:// doi.org/10.1...
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作者：Groathouse, Sean; Rassoul-Agha, Firas; Seppalainen, Timo; Sorensen, Evan
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison; Columbia University
摘要：We give an explicit description of a family of jointly invariant measures of the KPZ equation singled out by asymptotic slope conditions. These are couplings of Brownian motions with drift, and can be extended to a cadlag process indexed by all real drift parameters. We name this process the KPZ horizon (KPZH). As a corollary, we resolve a recent conjecture by showing the existence of a random, countably infinite dense set of drift values at which the Busemann process of the KPZ equation is di...
