-
作者：Miller, Jason; Sheffield, Scott
作者单位：Microsoft; Massachusetts Institute of Technology (MIT); University of Cambridge
摘要：Fix constants and , and let h be an instance of the Gaussian free field on a planar domain. We study flow lines of the vector field starting at a fixed boundary point of the domain. Letting vary, one obtains a family of curves that look locally like processes with (where ), which we interpret as the rays of a random geometry with purely imaginary curvature. We extend the fundamental existence and uniqueness results about these paths to the case that the paths intersect the boundary. We also sh...
-
作者：Procaccia, Eviatar B.; Rosenthal, Ron; Sapozhnikov, Artem
作者单位：University of California System; University of California Los Angeles; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove a quenched invariance principle for simple random walk on the unique infinite percolation cluster for a general class of percolation models on , , with long-range correlations introduced in (Drewitz et al. in J Math Phys 55(8):083307, 2014), solving one of the open problems from there. This gives new results for random interlacements in dimension at every level, as well as for the vacant set of random interlacements and the level sets of the Gaussian free field in the regime of the so...
-
作者：Duminil-Copin, Hugo; Manolescu, Ioan
作者单位：University of Geneva
摘要：We prove that random-cluster models with on a variety of planar lattices have a sharp phase transition, that is that there exists some parameter below which the model exhibits exponential decay and above which there exists a.s. an infinite cluster. The result may be extended to the Potts model via the Edwards-Sokal coupling. Our method is based on sharp threshold techniques and certain symmetries of the lattice; in particular it makes no use of self-duality. Part of the argument is not restric...
-
作者：Defosseux, Manon
作者单位：Universite Paris Cite
摘要：We construct a sequence of Markov processes on the set of dominant weights of an affine Lie algebra g considering tensor product of irreducible highest weight modules of g and specializations of the characters involving the Weyl vector.. We show that it converges towards a space-time Brownian motion with a drift, conditioned to remain in a Weyl chamber associated to the root system of g. This extends in particular the results of Defosseux (arXiv:1401.3115,2014) to any affine Lie algebras, in t...
-
作者：Last, Guenter; Peccati, Giovanni; Schulte, Matthias
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Luxembourg
摘要：We prove a new class of inequalities, yielding bounds for the normal approximation in the Wasserstein and the Kolmogorov distance of functionals of a general Poisson process (Poisson random measure). Our approach is based on an iteration of the classical Poincar, inequality, as well as on the use of Malliavin operators, of Stein's method, and of an (integrated) Mehler's formula, providing a representation of the Ornstein-Uhlenbeck semigroup in terms of thinned Poisson processes. Our estimates ...
-
作者：Andres, Sebastian; Deuschel, Jean-Dominique; Slowik, Martin
作者单位：University of Bonn; Technical University of Berlin
摘要：We establish elliptic and parabolic Harnack inequalities on graphs with unbounded weights. As an application we prove a local limit theorem for a continuous time random walk in an environment of ergodic random conductances taking values in satisfying some moment conditions.
-
作者：Jirak, Moritz
作者单位：Humboldt University of Berlin
摘要：Let be a stationary process with associated lag operators . Uniform asymptotic expansions of the corresponding empirical eigenvalues and eigenfunctions are established under almost optimal conditions on the lag operators in terms of the eigenvalues (spectral gap). In addition, the underlying dependence assumptions are optimal in a certain sense, including both short and long memory processes. This allows us to study the relative maximum deviation of the empirical eigenvalues under very general...
-
作者：Baur, Erich
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS)
摘要：We are concerned with random walks on , , in an i.i.d. random environment with transition probabilities -close to those of simple random walk. We assume that the environment is balanced in one fixed coordinate direction, and invariant under reflection in the coordinate hyperplanes. The invariance condition was used in Baur and Bolthausen (Ann Probab 2013, arXiv:1309.3169) as a weaker replacement of isotropy to study exit distributions. We obtain precise results on mean sojourn times in large b...
-
作者：Osada, Hirofumi; Shirai, Tomoyuki
作者单位：Kyushu University; Kyushu University
摘要：We prove a dichotomy between absolute continuity and singularity of the Ginibre point process and its reduced Palm measures , namely, reduced Palm measures and for and are mutually absolutely continuous if and only if ; they are singular each other if and only if . Furthermore, we give an explicit expression of the Radon-Nikodym density for dG(x)/dG(y) for x, y is an element of C-l.
-
作者：Attal, S.; Deschamps, J.; Pellegrini, C.
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; University of Genoa; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We study a particular class of complex-valued random variables and their associated random walks: complex obtuse random variables. They generalize, to the complex case, the real-valued obtuse random variables introduced in Equations de structure pour des martingales vectorielles. (S,minaire de Probabilit,s, XXVIII, p. 256278. Lecture Notes in Math., vol. 1583. Springer, Berlin (1994)) in order to understand the structure of normal martingales in . The extension to the complex case is motivated...
