-
作者：Pavlov, Ronnie
作者单位：University of British Columbia
摘要：For any two-dimensional nearest neighbor shift of finite type X and any integer n >= 1, one can define the horizontal strip shift H-n (X) to be the set of configurations on Z x {1, ... , n} which do not contain any forbidden pairs of adjacent letters for X. It is always the case that the sequence h(top)(H-n(X))/n of normalized topological entropies of the strip shifts converges to h(toP)(X), the topological entropy of X. In this paper, we combine ergodic theoretic techniques with methods from ...
-
作者：Aaronson, Jon
作者单位：Tel Aviv University
摘要：Relative complexity measures the complexity of a probability preserving transformation relative to a factor being a sequence of random variables whose exponential growth rate is the relative entropy of the extension. We prove distributional limit theorems for the relative complexity of certain zero entropy extensions: RWRSs whose associated random walks satisfy the alpha-stable CLT (1 < alpha <= 2). The results give invariants for relative isomorphism of these.
-
作者：Dette, Holger; Nagel, Jan
作者单位：Ruhr University Bochum; Technical University of Munich
摘要：In this paper we define distributions on moment spaces corresponding to measures on the real line with an unbounded support. We identify these distributions as limiting distributions of random moment vectors defined on compact moment spaces and as distributions corresponding to random spectral measures associated with the Jacobi, Laguerre and Hermite ensemble from random matrix theory. For random vectors on the unbounded moment spaces we prove a central limit theorem where the centering vector...
-
作者：Ledoux, M.
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Institut Universitaire de France
摘要：We analyze from the viewpoint of an abstract Markov operator recent results by Nualart and Peccati, and Nourdin and Peccati, on the fourth moment as a condition on a Wiener chaos to have a distribution close to Gaussian. In particular, we are led to introduce a notion of chaos associated to a Markov operator through its iterated gradients and present conditions on the (pure) point spectrum for a sequence of chaos eigenfunctions to converge to a Gaussian distribution. Convergence to gamma distr...
-
作者：Bendikov, Alexander; Saloff-Coste, Laurent
作者单位：University of Wroclaw; Cornell University
摘要：We study the decay of convolution powers of probability measures without second moment but satisfying some weaker finite moment condition. For any locally compact unimodular group G and any positive function rho : G --> [0, +infinity], we introduce a function Phi(G,rho) which describes the fastest possible decay of n bar right arrow phi((2n)) (e) when phi is a symmetric continuous probability density such that integral rho phi is finite. We estimate Phi(G,rho) for a variety of groups G and fun...
-
作者：Kuwae, Kazuhiro
作者单位：Kumamoto University
-
作者：Bhamidi, Shankar; van der Hofstad, Remco; van Leeuwaarden, Johan S. H.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Eindhoven University of Technology
摘要：We find scaling limits for the sizes of the largest components at criticality for rank-1 inhomogeneous random graphs with power-law degrees with power-law exponent tau. We investigate the case where tau is an element of (3,4), so that the degrees have finite variance but infinite third moment. The sizes of the largest clusters, resealed by n(-(tau-2)/(tau-1)), converge to hitting times of a thinned Levy process, a special case of the general multiplicative coalescents studied by Aldous [Ann. P...
-
作者：Beffara, V.; Duminil-Copin, H.
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); University of Geneva
摘要：In a recent and celebrated article, Smirnov [Ann. of Math. (2) 172 (2010) 1435-1467] defines an observable for the self-dual random-cluster model with cluster weight q = 2 on the square lattice Z(2), and uses it to obtain conformal invariance in the scaling limit. We study this observable away from the self-dual point. From this, we obtain a new derivation of the fact that the self-dual and critical points coincide, which implies that the critical inverse temperature of the Ising model equals ...
-
作者：Chen, Zhen-Qing; Kim, Panki; Song, Renming
作者单位：University of Washington; University of Washington Seattle; Seoul National University (SNU); University of Illinois System; University of Illinois Urbana-Champaign
摘要：Suppose that d >= 2 and alpha is an element of (1, 2). Let D be a bounded C-1,C-1 open set in R-d and b an R-d-valued function on R-d whose components are in a certain Kato class of the rotationally symmetric a-stable process. In this paper, we derive sharp two-sided heat kernel estimates for L-b = Delta(alpha/2) + b . del in D with zero exterior condition. We also obtain the boundary Harnack principle for L-b in D with explicit decay rate.
-
作者：Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider continuous time random interlacements on Z(d), d >= 3, and characterize the distribution of the corresponding stationary random field of occupation times. When d = 3, we relate this random field to the two-dimensional Gaussian free field pinned at the origin by looking at scaled differences of occupation times of long rods by random interlacements at appropriately tuned levels. In the main asymptotic regime, a scaling factor appears in the limit, which is independent of the free fi...
