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作者：Gueneysu, B.; Matte, O.; Moller, J. S.
作者单位：Humboldt University of Berlin; Aarhus University
摘要：We discuss Hilbert space-valued stochastic differential equations associated with the heat semi-groups of the standard model of non-relativistic quantum electrodynamics and of corresponding fiber Hamiltonians for translation invariant systems. In particular, we prove the existence of a stochastic flow satisfying the strong Markov property and the Feller property. To this end we employ an explicit solution ansatz. In the matrix-valued case, i.e., if the electron spin is taken into account, it i...
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作者：Cerny, Jiri; Wassmer, Tobias
作者单位：University of Vienna
摘要：We study the Metropolis dynamics of the simplest mean-field spin glass model, the random energy model. We show that this dynamics exhibits aging by showing that the properly rescaled time change process between the Metropolis dynamics and a suitably chosen 'fast' Markov chain converges in distribution to a stable subordinator. The rescaling might depend on the realization of the environment, but we show that its exponential growth rate is deterministic.
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作者：Hofmanova, Martina; Roeger, Matthias; von Renesse, Max
作者单位：Max Planck Society; Technical University of Berlin; Dortmund University of Technology; Leipzig University
摘要：We study a stochastically perturbed mean curvature flow for graphs in over the two-dimensional unit-cube subject to periodic boundary conditions. The stochastic perturbation is a one dimensional white noise acting uniformly in all points of the surface in normal direction. We establish the existence of a weak martingale solution. The proof is based on energy methods and therefore presents an alternative to the stochastic viscosity solution approach. To overcome difficulties induced by the dege...
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作者：Neuman, Eyal; Zheng, Xinghua
作者单位：University of Rochester; Hong Kong University of Science & Technology
摘要：We study the maximal displacement of a one dimensional subcritical branching random walk initiated by a single particle at the origin. For each let be the rightmost position reached by the branching random walk up to generation n. Under the assumption that the offspring distribution has a finite third moment and the jump distribution has mean zero and a finite probability generating function, we show that there exists such that the function
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作者：Gu, Yu
作者单位：Stanford University
摘要：In this paper, we study high order correctors in stochastic homogenization. We consider elliptic equations in divergence form on , with the random coefficients constructed from i.i.d. random variables. We prove moment bounds on the high order correctors and their gradients under dimensional constraints. It implies the existence of stationary correctors and stationary gradients in high dimensions. As an application, we prove a two-scale expansion of the solutions to the random PDE, which identi...
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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...
