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作者：Lawler, Gregory F.; Zhou, Wang
作者单位：University of Chicago; National University of Singapore
摘要：Developing the theory of two-sided radial and chordal SLE, we prove that the natural parametrization on SLE kappa curves is well defined for all kappa <8. Our proof uses a two-interior-point local martingale.
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作者：Gill, Hardeep
作者单位：University of British Columbia
摘要：We construct a supercritical interacting measure-valued diffusion with representative particles that are attracted to, or repelled from, the center of mass. Using the historical stochastic calculus of Perkins, we modify a super Ornstein-Uhlenbeck process with attraction to its origin, and prove continuum analogues of results of Englander [Electron. J. Probab. 15 (2010) 1938-1970] for binary branching Brownian motion. It is shown, on the survival set, that in the attractive case the mass normal...
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作者：Ivanov, Alexander V.; Leonenko, Nikolai; Ruiz-Medina, Maria D.; Savich, Irina N.
作者单位：Ministry of Education & Science of Ukraine; Igor Sikorsky Kyiv Polytechnic Institute; Cardiff University; University of Granada
摘要：The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This paper is motivated by its potential applications in nonlinear regression, and asymptotic inference on nonlinear functionals of Gaussian stationary processes with singular spectra.
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作者：Pene, Francoise; Saussol, Benoit; Zweimueller, Roland
作者单位：Universite de Bretagne Occidentale; University of Vienna
摘要：We consider random walks on the line given by a sequence of independent identically distributed jumps belonging to the strict domain of attraction of a stable distribution, and first determine the almost sure exponential divergence rate, as epsilon -> 0, of the return time to (-epsilon, epsilon). We then refine this result by establishing a limit theorem for the hitting-time distributions of (x - epsilon, x + epsilon) with arbitrary x is an element of R.
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作者：Wang, Yizao; Roy, Parthanil; Stoev, Stilian A.
作者单位：University of Michigan System; University of Michigan; Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：We establish characterization results for the ergodicity of stationary symmetric alpha-stable (S alpha S) and alpha-Frechet random fields. We show that the result of Samorodnitsky [Ann. Probab. 33 (2005) 1782-1803] remains valid in the multiparameter setting, that is, a stationary S alpha S (0 < alpha < 2) random field is ergodic (or, equivalently, weakly mixing) if and only if it is generated by a null group action. Similar results are also established for max-stable random fields. The key in...
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作者：Cator, Eric; Pimentel, Leandro P. R.
作者单位：Delft University of Technology; Universidade Federal do Rio de Janeiro
摘要：In this paper we will show how the results found in [Probab. Theory Related Fields 154 (2012) 89-125], about the Busemann functions in last-passage percolation, can be used to calculate the asymptotic distribution of the speed of a single second class particle starting from an arbitrary deterministic configuration which has a rarefaction fan, in either the totally asymetric exclusion process or the Hammersley interacting particle process. The method will be to use the well-known last-passage p...
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作者：Jung, Paul; Markowsky, Greg
作者单位：University of Alabama System; University of Alabama Birmingham; Monash University
摘要：For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the so-called iterated Brownian motion. Khoshnevisan and Lewis [Ann. Appl. Probab. 9 (1999) 629-667] suggested the existence of a form of measure-theoretic duality between iterated Brownian motion and a Brownian motion in random scenery. We show that a random walk ...
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作者：Sabot, Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We consider random walks in random Dirichlet environment (RWDE), which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On Z(d), RWDE are parameterized by a 2d-tuple of positive reals called weights. In this paper, we characterize for d >= 3 the weights for which there exists an absolutely continuous invariant probability distribution for the process viewed from the particle. We can deduce from this result ...
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作者：Calka, Pierre; Schreiber, Tomasz; Yukich, J. E.
作者单位：Universite de Rouen Normandie; Nicolaus Copernicus University; Lehigh University
摘要：Schreiber and Yukich [Ann. Probab. 36 (2008) 363-396] establish an asymptotic representation for random convex polytope geometry in the unit ball B-d, d >= 2, in terms of the general theory of stabilizing functionals of Poisson point processes as well as in terms of generalized paraboloid growth processes. This paper further exploits this connection, introducing also a dual object termed the paraboloid hull process. Via these growth processes we establish local functional limit theorems for th...
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作者：Dembo, Amir; Montanari, Andrea; Sun, Nike
作者单位：Stanford University; Stanford University; Stanford University
摘要：We consider homogeneous factor models on uniformly sparse graph sequences converging locally to a (unimodular) random tree T, and study the existence of the free energy density phi, the limit of the log-partition function divided by the number of vertices n as n tends to infinity. We provide a new interpolation scheme and use it to prove existence of, and to explicitly compute, the quantity phi subject to uniqueness of a relevant Gibbs measure for the factor model on T. By way of example we co...
