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作者：Meiners, Matthias; Mentemeier, Sebastian
作者单位：Technical University of Darmstadt; Dortmund University of Technology
摘要：We consider smoothing equations of the form X law = Sigma(j >= 1) TjXj + C where is a given sequence of random variables and are independent copies of X and independent of the sequence . The focus is on complex smoothing equations, i.e., the case where the random variables are complex-valued, but also more general multivariate smoothing equations are considered, in which the are similarity matrices. Under mild assumptions on , we describe the laws of all random variables X solving the above sm...
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作者：Leble, Thomas
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：The study of two-dimensional Coulomb gases lies at the interface of statistical physics and non-Hermitian random matrix theory. In this paper we give a large deviation principle (LDP) for the empirical fields obtained, under the canonical Gibbs measure, by zooming around a point in the bulk of the equilibrium measure, up to the finest averaging scale . The rate function is given by the sum of the renormalized energy of Serfaty et al. weighted by the inverse temperature, and of the specific rel...
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作者：Benaim, Michel; Gauthier, Carl-Erik
作者单位：University of Neuchatel
摘要：Let M be a compact connected oriented Riemannian manifold. The purpose of this paper is to investigate the long time behavior of a degenerate stochastic differential equation on the state space M x R-n; which is obtained via a natural change of variable from a self-repelling diffusion taking the form dX(t) = sigma dB(t)(X-t) - integral(t)(0) del V-Xs (X-t)dsdt, X-0 = x where {B-t} is a Brownian vector field on M, sigma > 0 and V-x(y) = V(x, y) is a diagonal Mercer kernel. We prove that the ind...
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作者：Bhamidi, Shankar; Sen, Sanchayan; Wang, Xuan
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology
摘要：The last few years have witnessed tremendous interest in understanding the structure as well as the behavior of dynamics for inhomogeneous random graph models to gain insight into real-world systems. In this study we analyze the maximal components at criticality of one famous class of such models, the rank-one inhomogeneous random graph model (Norros and Reittu, Adv Appl Probab 38(1):59-75, 2006; Bollobas et al., Random Struct Algorithms 31(1):3-122, 2007, Section 16.4). Viewing these componen...
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作者：Ramirez, Jose A.; Rider, Brian
作者单位：Universidad Costa Rica; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：We characterize the limiting smallest eigenvalue distributions (or hard edge laws) for sample covariance type matrices drawn from a spiked population. In the case of a single spike, the results are valid in the context of the general ensembles. For multiple spikes, the necessary construction restricts matters to real, complex or quaternion ( or 4) ensembles. The limit laws are described in terms of random integral operators, and partial differential equations satisfied by the corresponding dis...
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作者：[Anonymous]
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作者：Blanca, Antonio; Sinclair, Alistair
作者单位：University of California System; University of California Berkeley
摘要：The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paper we analyze the Glauber dynamics of the random-cluster model in the canonical case where the underlying graph is an box in the Cartesian lattice . Our main result is a upper bound for the mixing time at all values of the model parameter p except the critical point , and for all values of the second...
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作者：Crane, Harry
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：The transition law of every exchangeable Feller process on the space of countable graphs is determined by a -finite measure on the space of -valued arrays. In discrete time, this characterization gives rise to a construction from an independent, identically distributed sequence of exchangeable random functions. In continuous time, the behavior is enriched by a L,vy-It-Khintchine-type decomposition of the jump measure into mutually singular components that govern global, vertex-level, and edge-...
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作者：Ceillier, Gael; Leuridan, Christophe
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：Let X be a stationary process with values in some -finite measured state space , indexed by . Call its natural filtration. In Ceillier (Ann Probab 40(5):1980-2007, 2012), sufficient conditions were given for to be standard when E is finite, and the proof used a coupling of all probabilities on the finite set E. In this paper, we construct a coupling of all laws having a density with regard to , which is much more involved. Then, we provide sufficient conditions for to be standard, generalizing...
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作者：Grama, Ion; Le Page, Emile; Peigne, Marc
摘要：Let g1, g2,... be i. i. d. random matrices in GL (d, R). For any n >= 1 consider the product G(n) = g(n) ... g(1) and the random process G(n)v = g(n) ... g(1)v in R-d starting at point v is an element of R-d \ {0}. It is well known that under appropriate assumptions, the sequence (log ||G(n)v||) (n >= 1) behaves like a sum of i. i. d. r. v.' s and satisfies standard classical properties such as the law of large numbers, the law of iterated logarithm and the central limit theorem. For any vecto...
