-
作者：Biskamp, Moritz
作者单位：Technical University of Berlin
摘要：It has been shown by various authors that the diameter of a given nontrivial bounded connected set X grows linearly in time under the action of an isotropic Brownian flow (IBF), which has a nonnegative top-Lyapunov exponent. In case of a planar IBF with a positive top-Lyapunov exponent, the precise deterministic linear growth rate K of the diameter is known to exist. In this paper we will extend this result to an asymptotic support theorem for the time-scaled trajectories of a planar IBF phi, ...
-
作者：Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We study a family of n-dimensional diffusions, taking values in the unit simplex of vectors with nonnegative coordinates that add up to one. These processes satisfy stochastic differential equations which are similar to the ones for the classical Wright-Fisher diffusions, except that the mutation rates are now nonpositive. This model, suggested by Aldous, appears in the study of a conjectured diffusion limit for a Markov chain on Cladograms. The striking feature of these models is that the bou...
-
作者：Kallenberg, Olav
作者单位：Auburn University System; Auburn University
摘要：Consider a locally finite Dawson-Watanabe superprocess xi = (xi(t)) in R-d with d >= 2. Our main results include some recursive formulas for the moment measures of xi, with connections to the uniform Brownian tree, a Brownian snake representation of Palm measures, continuity properties of conditional moment densities, leading by duality to strongly continuous versions of the multivariate Palm distributions, and a local approximation of xi(t) by a stationary cluster (eta) over tilde with nice c...
-
作者：Tan, Xiaolu; Touzi, Nizar
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the continuous semimartingale. The optimal transportation problem minimizes the cost among all continuous semimartingales with given initial and terminal distributions. Our first main result is an extension of the Kantorovitch duality to this context. We also suggest a ...
-
作者：Asselah, Amine; Gaudilliere, Alexandre
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when reaching a site that is not occupied by previous walks. It is known that the asymptotic shape of the cluster is a sphere. When the dimension is two or more, we have shown in a previous paper that the inner (resp., outer) fluctuations of its radius is at most of...
-
作者：Tugaut, Julian
作者单位：University of Bielefeld
摘要：We investigate the convergence of McKean-Vlasov diffusions in a non-convex landscape. These processes are linked to nonlinear partial differential equations. According to our previous results, there are at least three stationary measures under simple assumptions. Hence, the convergence problem is not classical like in the convex case. By using the method in Benedetto et al. [J. Statist. Phys. 91 (1998) 1261-1271] about the monotonicity of the free-energy, and combining this with a complete des...
-
作者：Angel, Omer; Goodman, Jesse; Merle, Mathieu
作者单位：University of British Columbia; Leiden University - Excl LUMC; Leiden University; Universite Paris Cite
摘要：We prove existence of the scaling limit of the invasion percolation cluster (IPC) on a regular tree. The limit is a random real tree with a single end. The contour and height functions of the limit are described as certain diffusive stochastic processes. This convergence allows us to recover and make precise certain asymptotic results for the MC. In particular, we relate the limit of the rescaled level sets of the MC to the local time of the scaled height function.
-
作者：Xiong, Jie
作者单位：University of Tennessee System; University of Tennessee Knoxville; University of Macau
摘要：A stochastic partial differential equation (SPDE) is derived for super-Brownian motion regarded as a distribution function valued process. The strong uniqueness for the solution to this SPDE is obtained by an extended Yamada-Watanabe argument. Similar results are also proved for the Fleming-Viot process.
-
作者：Meyerovitch, Tom
作者单位：Ben-Gurion University of the Negev
摘要：In this paper we study the Poisson process over a a-finite measure-space equipped with a measure preserving transformation or a group of measure preserving transformations. For a measure-preserving transformation T acting on a a-finite measure-space X, the Poisson suspension of T is the associated probability preserving transformation T-* which acts on realization of the Poisson process over X. We prove ergodicity of the Poisson-product T x T-* under the assumption that T is ergodic and conser...
-
作者：Grimmett, Geoffrey R.; Manolescu, Ioan
作者单位：University of Cambridge
摘要：The star triangle transformation is used to obtain an equivalence extending over the set of all (in)homogeneous bond percolation models on the square, triangular and hexagonal lattices. Among the consequences are box-crossing (RSW) inequalities for such models with parameter-values at which the transformation is valid. This is a step toward proving the universality and conformality of these processes. It implies criticality of such values, thereby providing a new proof of the critical point of...
