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作者：Peltola, Eveliina; Wu, Hao
作者单位：Aalto University; Tsinghua University
摘要：We prove that in the scaling limit, the crossing probabilities of multiple interfaces in the critical planar Ising model with alternating boundary condi-tions are conformally invariant expressions given by the pure partition func-tions of multiple SLE & kappa; with & kappa; = 3. In particular, this identifies the scaling limits with ratios of specific correlation functions of conformal field theory.
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作者：Ding, Xiucai; Ji, Hong Chang
作者单位：University of California System; University of California Davis; Institute of Science & Technology - Austria
摘要：Consider the random matrix model A1/2UB U*A1/2, where A and B are two N x N deterministic matrices and U is either an N x N Haar unitary or orthogonal random matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991) 201-220), the limiting empirical spectral distribu-tion (ESD) of the above model is given by the free multiplicative convolution of the limiting ESDs of A and B, denoted as & mu;& alpha; & REG; & mu;⠃, where & mu;& alpha; and & mu;⠃ are the limiting ESDs of...
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作者：Qiu, Jiaze; Sen, Subhabrata
作者单位：Harvard University
摘要：We derive a variational representation for the log-normalizing constant of the posterior distribution in Bayesian linear regression with a uniform spherical prior and an i.i.d. Gaussian design. We work under the propor-tional asymptotic regime, where the number of observations and the number of features grow at a proportional rate. Our representation holds when the variance of the additive noise is sufficiently large, which corresponds to a high-temperature condition in statistical physics. Th...
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作者：Banerjee, Sayan; Bhamidi, Shankar; Carmichael, Iain
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of California System; University of California Berkeley
摘要：We consider dynamic random trees constructed using an attachment function f : N & RARR; R+ where, at each step of the evolution, a new vertex attaches to an existing vertex v in the current tree with probability propor-tional to f (degree(v)). We explore the effect of a change point in the sys-tem; the dynamics are initially driven by a function f until the tree reaches size & tau;(n) & ISIN; (0, n), at which point the attachment function switches to another function, g, until the tree reaches...
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作者：Rollin, Adrian; Zhang, Zhuo-Song
作者单位：National University of Singapore; Southern University of Science & Technology
摘要：Time-evolving random graph models have appeared and have been studied in various fields of research over the past decades. However, the rigorous mathematical treatment of large graphs and their limits at the process-level is still in its infancy. In this article, we adapt the approach of Athreya, den ting of multigraphs and multigraphons, introduced by Kolossvary and Rath (Acta Math. Hungar. 130 (2011) 1-34). We then generalise the work of Rath namics on the configuration model-in contrast to ...
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作者：Chen, Yong; Duan, Jinqiao; Gao, Hongjun
作者单位：Zhejiang Sci-Tech University; Illinois Institute of Technology; Southeast University - China
摘要：We study the global well-posedness and wave-breaking phenomenon for the stochastic rotation-two-component Camassa-Holm (R2CH) system. First, we find a Hamiltonian structure of the R2CH system and use the stochastic Hamiltonian to derive the stochastic R2CH system. Then, we establish the local well-posedness of the stochastic R2CH system using a dispersion-dissipation approximation system and the regularization method. We also show a precise blow-up criterion for the stochastic R2CH system. Mor...
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作者：Feng, Xinwei; Hu, Ying; Huang, Jianhui
作者单位：Shandong University; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); Hong Kong Polytechnic University
摘要：This paper aims to systematically solve stochastic team optimization of a large-scale system, in a linear-quadratic-Gaussian framework. Concretely, the underlying large-scale system involves considerable weakly coupled co-operative agents for which the individual admissible controls: (i) enter the diffusion terms, (ii) are constrained in some closed-convex subsets and (iii) subject to a general partial decentralized information structure. A more im-portant but serious feature: (iv) all agents ...
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作者：Djehiche, Boualem; Elie, Romuald; Hamadene, Said
作者单位：Royal Institute of Technology; Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Le Mans Universite
摘要：In this paper, we study a class of reflected backward stochastic differen-tial equations (BSDEs) of mean-field type, where the mean-field interaction in terms of the distribution of the Y-component of the solution enters in both the driver and the lower obstacle. We consider in details the case where the lower obstacle is a deterministic function of (Y, E[Y]) and discuss the more general dependence on the distribution of Y. Under mild Lipschitz and in-tegrability conditions on the coefficients...
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作者：Charlier, Christophe; Moreillon, Philippe
作者单位：Royal Institute of Technology
摘要：The Pearcey process is a universal point process in random matrix theory. In this paper, we study the generating function of the Pearcey process on any number m of intervals. We derive an integral representation for it in terms of a Hamiltonian that is related to a system of 6m + 2 coupled nonlinear equations. We also obtain asymptotics for the generating function as the size of the intervals get large, up to and including the constant term. This work generalizes some results of Dai, Xu, and Z...
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作者：Hilario, Marcelo R.; Sa, Marcos; Sanchis, Remy; Teixeira, Augusto
作者单位：Universidade Federal de Minas Gerais; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Let {& xi;i}i & GE;1 be a sequence of i.i.d. positive random variables. Starting from the usual square lattice replace each horizontal edge that links a site in the ith vertical column to another in the (i + 1)th vertical column by an edge having length & xi;i. Then declare independently each edge e in the resulting lattice open with probability pe = p|e| where p & ISIN; [0, 1] and |e| is the length of e. We relate the occurrence of a nontrivial phase transition for this model to moment proper...
