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作者：Chazottes, J. -R.; Collet, P.; Meleard, S.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study a general class of birth-and-death processes with state space N that describes the size of a population going to extinction with probability one. This class contains the logistic case. The scale of the population is measured in terms of a 'carrying capacity' K. When K is large, the process is expected to stay close to its deterministic equilibrium during a long time but ultimately goes extinct. Our aim is to quantify the behavior of the process and the mean time to extinction in the q...
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作者：Bernardin, Cedric; Goncalves, Patricia; Sethuraman, Sunder
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); Universidade do Minho; University of Arizona
摘要：With respect to a class of long-range exclusion processes on , with single particle transition rates of order , starting under Bernoulli invariant measure with density , we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals. Part of our motivation is to investigate the dependence on , d and with respect to the variance of these functionals and associated scaling limits. In the case the rates are symmetric, among other results, we find the sc...
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作者：Bloemendal, Alex; Knowles, Antti; Yau, Horng-Tzer; Yin, Jun
作者单位：Harvard University; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Wisconsin System; University of Wisconsin Madison
摘要：We introduce a class of M x M sample covariance matrices Q which subsumes and generalizes several previous models. The associated population covariance matrix Sigma = EQ is assumed to differ from the identity by a matrix of bounded rank. All quantities except the rank of Sigma - I-M may depend on M in an arbitrary fashion. We investigate the principal components, i. e. the top eigenvalues and eigenvectors, of Q. We derive precise large deviation estimates on the generalized components < w, xi(...
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作者：Zhan, Dapeng
作者单位：Michigan State University
摘要：We first prove that, for kappa is an element of (0, 4), a whole-plane SLE(kappa; kappa + 2) trace stopped at a fixed capacity time satisfies reversibility. We then use this reversibility result to prove that, for kappa is an element of(0, 4), a chordal SLE kappa curve stopped at a fixed capacity time can be mapped conformally to the initial segment of a whole-plane SLE(kappa; kappa+ 2) trace. A similar but weaker result holds for radial SLE.. These results are then used to study the ergodic be...
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作者：Comets, Francis; Vu-Lan Nguyen
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：Consider the directed polymer in one space dimension in log-gamma environment with boundary conditions, introduced by Seppalainen (Ann Probab, 40(1):19-73, 2012). In the equilibrium case, we prove that the end point of the polymer converges in law as the length increases, to a density proportional to the exponent of a zero-mean random walk. This holds without space normalization, and the mass concentrates in a neighborhood of the minimum of this random walk. We have analogous results out of eq...
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作者：van de Brug, Tim; Camia, Federico; Lis, Marcin
作者单位：Vrije Universiteit Amsterdam; New York University; New York University Abu Dhabi; Chalmers University of Technology; University of Gothenburg
摘要：The random walk loop soup is a Poissonian ensemble of lattice loops; it has been extensively studied because of its connections to the discrete Gaussian free field, but was originally introduced by Lawler and Trujillo Ferreras as a discrete version of the Brownian loop soup of Lawler and Werner, a conformally invariant Poissonian ensemble of planar loops with deep connections to conformal loop ensembles (CLEs) and the Schramm-Loewner evolution (SLE). Lawler and Trujillo Ferreras showed that, r...
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作者：Basse-O'Connor, Andreas; Rosinski, Jan
作者单位：Aarhus University; University of Tennessee System; University of Tennessee Knoxville
摘要：Stricker's theorem states that a Gaussian process is a semimartingale in its natural filtration if and only if it is the sum of an independent increment Gaussian process and a Gaussian process of finite variation, see Stricker (ZWahrsch Verw Geb 64(3):303-312, 1983). We consider extensions of this result to non Gaussian infinitely divisible processes. First we show that the class of infinitely divisible semimartingales is so large that the natural analog of Stricker's theorem fails to hold. Th...
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作者：Nickl, Richard; Reiss, Markus; Soehl, Jakob; Trabs, Mathias
作者单位：University of Cambridge; Humboldt University of Berlin
摘要：Donsker-type functional limit theorems are proved for empirical processes arising from discretely sampled increments of a univariate Levy process. In the asymptotic regime the sampling frequencies increase to infinity and the limiting object is a Gaussian process that can be obtained from the composition of a Brownian motion with a covariance operator determined by the Levy measure. The results are applied to derive the asymptotic distribution of natural estimators for the distribution functio...
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作者：Balister, Paul; Bollobas, Bela; Smith, Paul
作者单位：University of Memphis
摘要：We study the distribution of the percolation time T of 2-neighbour bootstrap percolation on with initial set . We determine T up to a constant factor with high probability for all p above the critical probability for percolation, and to within a factor for a large range of p.
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作者：Benes, Christian; Lawler, Gregory F.; Viklund, Fredrik
作者单位：City University of New York (CUNY) System; Brooklyn College (CUNY); University of Chicago; Royal Institute of Technology; Uppsala University
摘要：We consider loop-erased random walk (LERW) running between two boundary points of a square grid approximation of a planar simply connected domain. The LERW Green's function is the probability that the LERW passes through a given edge in the domain. We prove that this probability, multiplied by the inverse mesh size to the power 3/4, converges in the lattice size scaling limit to (a constant times) an explicit conformally covariant quantity which coincides with the Green's function. The proof d...
