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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.
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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.
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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...
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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...
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作者：Hairer, Martin; Pillai, Natesh S.
作者单位：University of Warwick; Harvard University
摘要：We consider differential equations driven by rough paths and study the regularity of the laws and their long time behavior. In particular, we focus on the case when the driving noise is a rough path valued fractional Brownian motion with Hurst parameter H is an element of (1/3, 1/2]. Our contribution in this work is twofold. First, when the driving vector fields satisfy Hormander's celebrated Lie bracket condition, we derive explicit quantitative bounds on the inverse of the Malliavin matrix. ...
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作者：Inahama, Yuzuru
作者单位：Nagoya University
摘要：We consider a rough differential equation indexed by a small parameter epsilon > 0. When the rough differential equation is driven by fractional Brownian motion with Hurst parameter H (1/4 < H < 1/2), we prove the Laplace-type asymptotics for the solution as the parameter 8 tends to zero.
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作者：Brieussel, Jeremie
作者单位：Kyoto University
摘要：A variety of behaviors of entropy functions of random walks on finitely generated groups is presented, showing that for any 1/2 <= alpha <= beta <= 1, there is a group Gamma with measure mu equidistributed on a finite generating set such that lim inf log H-Gamma,H-mu(n)/log n = alpha, lim sup H-Gamma,H-mu(n)/log n = beta The groups involved are finitely generated subgroups of the group of automorphisms of an extended rooted tree. The return probability and the drift of a simple random walk Y-n...
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作者：Georgiou, Nicos; Seppaelaeinen, Timo
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explicit formulas for the 1 + 1-dimensional exactly solvable case with log-gamma distributed random weights. Along the way we establish some regularity results for this rate function for general distributions in arbitrary dimensions.
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作者：Lyons, Russell
作者单位：Indiana University System; Indiana University Bloomington
摘要：We extend the theory of distance (Brownian) covariance from Euclidean spaces, where it was introduced by Szekely, Rizzo and Bakirov, to general metric spaces. We show that for testing independence, it is necessary and sufficient that the metric space be of strong negative type. In particular, we show that this holds for separable Hilbert spaces, which answers a question of Kosorok. Instead of the manipulations of Fourier transforms used in the original work, we use elementary inequalities for ...
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作者：Berti, Patrizia; Pratelli, Luca; Rigo, Pietro
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：Let S be a Polish space and (X-n : n >= 1) an exchangeable sequence of S-valued random variables. Let alpha(n)(.) = P(Xn+1 is an element of E . vertical bar X-1, ... X-n) be the preweak dictive measure and a a random probability measure on S such that an alpha(n) -> weak alpha a.s. Two (related) problems are addressed. One is to give conditions for alpha << lambda a.s., where lambda is a (nonrandom) sigma-finite Borel measure on S. Such conditions should concern the finite dimensional distribu...
