Probability Theory and Related Fields

最新文章

• Gaussian curvature on random planar maps and Liouville quantum gravity AI翻译
  作者：Hip, Andres A. Contreras; Gwynne, Ewain
  作者单位：University of Chicago
  摘要：We investigate the notion of curvature in the context of Liouville quantum gravity (LQG) surfaces. We define the Gaussian curvature for LQG, which we conjecture is the scaling limit of discrete curvature on random planar maps. Motivated by this, we study asymptotics for the discrete curvature of & varepsilon;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength...
• An alternative approach for the mean-field behaviour of weakly self-avoiding walks in dimensions d > 4 AI翻译
  作者：Duminil-Copin, Hugo; Panis, Romain
  作者单位：Universite Paris Saclay; University of Geneva
  摘要：This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions d > 4. Among other results, we obtain up-to-constant estimates for the full-space and half-space two-point functions in the critical and near-critical regimes. A companion paper proposes a similar analysis for spread-out Bernoulli percolation in dimensions d > 6 [10].
• On invariant distributions of Feller Markov chains with applications to dynamical systems with random switching (vol 192, pg 1283, 2025) AI翻译
  作者：Benaim, Michel; Tough, Oliver
  作者单位：University of Neuchatel; University of Bath
• KPZ exponents for the half-space log-gamma polymer AI翻译
  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...
• Moment generating functions and moderate deviation principles for lacunary sums AI翻译
  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...
• Geodesic Lévy flights and expected stopping time for random searches AI翻译
  作者：Chaubet, Yann; Bonthonneau, Yannick Guedes; Lefeuvre, Thibault; Tzou, Leo
  作者单位：University of Cambridge; Universite Paris 13; Universite Paris Cite; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); University of Amsterdam
  摘要：We give an analytic description for the infinitesimal generator constructed in Applebaum and Estrade (Ann Probab 28(1):166-184, 2000) for L & eacute;vy flights on a broad class of closed Riemannian manifolds including all negatively-curved manifolds, the flat torus and the sphere. Various properties of the associated semigroup and the asymptotics of the expected stopping time for L & eacute;vy flight based random searches for small targets, also known as the narrow capture problem, are then ob...
• Randomness and early termination: What makes a game exciting? AI翻译
  作者：Guo, Gaoyue; Howison, Sam D.; Possamai, Dylan; Reisinger, Christoph
  作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); University of Oxford; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：In this paper we revisit an open problem posed by Aldous on the max-entropy win-probability martingale: given two players of equal strength, such that the win-probability is a martingale diffusion, which of these processes has maximum entropy and hence gives the most excitement for the spectators? Our construction is based on the detailed study of a terminal-boundary value problem for the nonlinear parabolic PDE 2 partial derivative te(t,x)=log(-partial derivative xxe(t,x))\documentclass[12pt]...
• A uniform Dvoretzky-Kiefer-Wolfowitz inequality AI翻译
  作者：Bartl, Daniel; Mendelson, Shahar
  作者单位：National University of Singapore; National University of Singapore; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：We show that under minimal assumptions on a class of functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {H}$$\end{document} defined on a probability space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackag...
• Metastability between the clicks of Muller's ratchet AI翻译
  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. ...
• The giant component of excursion sets of spherical Gaussian ensembles: existence, uniqueness, and volume concentration AI翻译
  作者：Muirhead, Stephen; Wigman, Igor
  作者单位：University of Melbourne; University of London; King's College London; Monash University
  摘要：We establish the existence and uniqueness of a well-concentrated giant component in the supercritical excursion sets of three important ensembles of spherical Gaussian random fields: Kostlan's ensemble, band-limited ensembles, and the random spherical harmonics. Our main results prescribe quantitative bounds for the volume fluctuations of the giant that are essentially optimal for non-monochromatic ensembles, and suboptimal but still strong for monochromatic ensembles. Our results support the ...