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作者：Budhiraja, Amarjit; Wu, Ruoyu
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas the second describes a collection of pure jump Markov processes with a countable state space. For both cases the moderate deviation principle is formulated in terms of a large deviation principle (LDP), with an appropriate speed function, for suitably centered...
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作者：Subag, Eliran; Zeitouni, Ofer
摘要：Recently, sharp results concerning the critical points of the Hamiltonian of the p-spin spherical spin glass model have been obtained by means of moments computations. In particular, these moments computations allow for the evaluation of the leading term of the ground-state, i.e., of the global minimum. In this paper, we study the extremal point process of critical points-that is, the point process associated to all critical values in the vicinity of the ground-state. We show that the latter c...
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作者：Fitzner, Robert; van der Hofstad, Remco
作者单位：Eindhoven University of Technology
摘要：The lace expansion is a powerful perturbative technique to analyze the critical behavior of random spatial processes such as the self-avoiding walk, percolation and lattice trees and animals. The non-backtracking lace expansion (NoBLE) is a modification that allows us to improve its applicability in the nearest-neighbor setting on the -lattice for percolation, lattice trees and lattice animals. The NoBLE gives rise to a recursive formula that we study in this paper at a general level. We state...
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作者：Fehrman, Benjamin J.
作者单位：Max Planck Society
摘要：The results of this paper build upon those first obtained by Sznitman and Zeitouni (Invent Math 164(3), 455-567, 2006). We establish, for spacial dimensions , the existence of a unique invariant measure for isotropic diffusions in random environment on which are small perturbations of Brownian motion. Furthermore, we establish a general homogenization result for initial data which are locally measurable with respect to the coefficients.
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作者：Belius, David; Kistler, Nicola
作者单位：New York University; Goethe University Frankfurt
摘要：The -cover time of the two dimensional torus by Brownian motion is the time it takes for the process to come within distance from any point. Its leading order in the small -regime has been established by Dembo et al. (Ann Math 160:433-464, 2004). In this work, the second order correction is identified. The approach relies on a multi-scale refinement of the second moment method, and draws on ideas from the study of the extremes of branching Brownian motion.
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作者：Schapira, Bruno; Valesin, Daniel
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; University of Groningen
摘要：We consider the contact process on finite and connected graphs and study the behavior of the extinction time, that is, the amount of time that it takes for the infection to disappear in the process started from full occupancy. We prove, without any restriction on the graph G, that if the infection rate is larger than the critical rate of the one-dimensional process, then the extinction time grows faster than for any constant , where |G| denotes the number of vertices of G. Also for general gra...
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作者：Izyurov, Konstantin
作者单位：University of Helsinki
摘要：We prove a general result on convergence of interfaces in the critical planar Ising model to conformally invariant curves absolutely continuous with respect to SLE(3). Our setup includes multiple interfaces on arbitrary finitely connected domains, and we also treat the radial SLE case. In the case of simply and doubly connected domains, the limiting processes are described explicitly in terms of rational and elliptic functions, respectively.
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作者：Miller, Jason; Wu, Hao
作者单位：University of Cambridge; University of Geneva
摘要：We compute the almost-sure Hausdorff dimension of the double points of chordal for , confirming a prediction of Duplantier-Saleur (1989) for the contours of the FK model. We also compute the dimension of the cut points of chordal for as well as analogous dimensions for the radial and whole-plane processes for . We derive these facts as consequences of a more general result in which we compute the dimension of the intersection of two flow lines of the formal vector field , where h is a Gaussian...
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作者：Asselah, Amine; Schapira, Bruno
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the boundary of the range of simple random walk on in the transient case . We show that volumes of the range and its boundary differ mainly by a martingale. As a consequence, we obtain an upper bound on the variance of order in dimension three. We also establish a Central Limit Theorem in dimension four and larger.
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作者：Dembo, Amir; Mukherjee, Sumit
作者单位：Stanford University; Columbia University
摘要：Suppose the auto-correlations of real-valued, centered Gaussian process are non-negative and decay as for some regularly varying at infinity of order . With its primitive, we show that the persistence probabilities decay rate of is precisely of order , thereby closing the gap between the lower and upper bounds of Newell and Rosenblatt (Ann. Math. Stat. 33:1306-1313, 1962), which stood as such for over fifty years. We demonstrate its usefulness by sharpening recent results of Sakagawa (Adv. App...
