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作者：Ding, Jian; Song, Jian; Sun, Rongfeng
作者单位：Peking University; Shandong University; Shandong University; National University of Singapore
摘要：We study ferromagnetic Ising models on finite graphs with an inhomogeneous external field, where a subset of vertices is designated as the boundary. We show that the influence of boundary conditions on any given spin is maximised when the external field is identically 0. One corollary is that spin-spin correlations are maximised when the external field vanishes and the boundary condition is free, which proves a conjecture of Shlosman. In particular, the random field Ising model on Z(d), d >= 3...
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作者：Foondun, Mohammud; Joseph, Mathew; Kim, Kunwoo
作者单位：University of Strathclyde; Indian Statistical Institute; Indian Statistical Institute Bangalore; Pohang University of Science & Technology (POSTECH)
摘要：We consider the stochastic heat equation on [0, 1] with periodic boundary conditions and driven by space-time white noise. Under various natural conditions, we study small ball probabilities for the Holder semi-norms of the solutions, and provide near optimal bounds on these probabilities. As an application, we prove a support theorem in these Holder semi-norms.
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作者：Hoshino, Masato; Kawabi, Hiroshi; Kusuoka, Seiichiro
作者单位：University of Osaka; Keio University; Kyoto University
摘要：The present paper is a continuation of our previous work (Hoshino et al., J Evol Equ 21:339-375,2021) on the stochastic quantization of the exp(Phi)(2)-quantum field model on the two-dimensional torus. Making use of key properties of Gaussian multiplicative chaos and refining the method for singular SPDEs introduced in the previous work, we construct a unique time-global solution to the corresponding parabolic stochastic quantization equation in the full L-1 -regime vertical bar alpha vertical...
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作者：Regts, Guus
作者单位：University of Amsterdam
摘要：In this paper we show that absence of complex zeros of the partition function of the hard-core model on any family of bounded degree graphs that is closed under taking induced subgraphs implies that the associated probability measure, the hard-core measure, satisfies strong spatial mixing on that family. As a corollary we obtain that the hard-core measure on the family of bounded degree claw-free graphs satisfies strong spatial mixing for every value of the fugacity parameter. We furthermore d...
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作者：Boursier, Jeanne; Chafai, Djalil; Labbe, Cyril
作者单位：Universite PSL; Universite Paris-Dauphine; 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 PSL; Ecole Normale Superieure (ENS); Universite Paris Cite
摘要：We study the Dyson-Ornstein-Uhlenbeck diffusion process, an evolving gas of interacting particles. Its invariant law is the beta Hermite ensemble of random matrix theory, a non-product log-concave distribution. We explore the convergence to equilibrium of this process for various distances or divergences, including total variation, relative entropy, and transportation cost. When the number of particles is sent to infinity, we show that a cutoff phenomenon occurs: the distance to equilibrium va...
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作者：Croydon, D. A.; Shiraishi, D.
作者单位：Kyoto University
摘要：We correct a proof in the article 'D. Shiraishi, Exact value of the resistance exponent for four dimensional random walk trace, Probab. Theory and Related Fields 153 (2012), no. 1-2, 191-232'.
