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作者：Baxendale, Peter H.
作者单位：University of Southern California
摘要：This paper considers the effect of additive white noise on the normal form for the supercritical Hopf bifurcation in 2 dimensions. The main results involve the asymptotic behavior of the top Lyapunov exponent lambda associated with this random dynamical system as one or more of the parameters in the system tend to 0 or infinity. This enablesthe construction of a bifurcation diagram in parameter space showing stable regionswhere lambda<0 (implying synchronization) and unstable regions where lam...
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作者：Devlin, Charles
作者单位：University of Chicago
摘要：Liouville first passage percolation (LFPP) with parameter xi > 0 is the family of random distance functions (metrics) (D-h(is an element of))is an element of > 0 on obtained heuristically by integrating e(xi h) along paths, where h is a variant of the Gaussian free field. There is a critical value xi(crit )approximate to 0.41 such that for xi is an element of (0, xi(crit)), appropriately rescaled LFPP converges in probability uniformly on compact subsets of C to a limiting metric D-h on gamma-...
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作者：Tempelmayr, Markus
作者单位：University of Munster
摘要：We give a novel characterization of the centered model in regularity structures which persists for rough drivers even as a mollification fades away. We present our result for a class of quasilinear equations driven by noise, however we believe that the method is robust and applies to a much broader class of subcritical equations. Furthermore, we prove that a convergent sequence of noise ensembles, satisfying uniformly a spectral gap assumption, implies the corresponding convergence of the asso...
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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：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...
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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]...
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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...
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作者：Amorino, Chiara; Belomestny, Denis; Pilipauskaite, Vytaute; Podolskij, Mark; Zhou, Shi-Yuan
作者单位：Pompeu Fabra University; Barcelona School of Economics; Aalborg University; University of Luxembourg
摘要：This paper investigates the estimation of the interaction function for a class of McKean-Vlasov stochastic differential equations. The estimation is based on observations of the associated particle system at time T, considering the scenario where both the time horizon T and the number of particles N tend to infinity. Our proposed method recovers polynomial rates of convergence for the resulting estimator. This is achieved under the assumption of exponentially decaying tails for the interaction...
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作者：Chen, Xin; Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian
作者单位：Shanghai Jiao Tong University; University of Washington; University of Washington Seattle; Waseda University; Fujian Normal University; Fujian Normal University; Fujian Normal University
摘要：We consider random conductance models with long range jumps on Z(d), where the one-step transition probability from x to y is proportional to w( x,y) | x - y | (-d-alpha )with alpha is an element of ( 0 , 2). Assume that {w x,y } (x,y)is an element of E are independent, identically distributed and uniformly bounded non-negative random variables with E w(x,y) = 1, where E is the set of all unordered pairs on Z(d). We obtain a quantitative version of stochastic homogenization for these random wa...
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作者：Gamarnik, David; Jagannath, Aukosh; Kizildag, Eren C.
作者单位：Massachusetts Institute of Technology (MIT); University of Waterloo; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We study the Isingp-spin glass model for largep. We show that for any inversetemperature root ln 2infinity, there exists exponentially many well-separated clusters such that(a) each cluster has exponentially small Gibbs mass, and (b) the clusters collectivelycontain all but a vanishing fraction of Gibbs mass. Moreover, these clusters consist ofconfigurations with energy near beta. Range of temperatures for which shattering occursis within thereplica symmetricregion. To the best of our knowledg...
