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作者：Cerf, Raphael
作者单位：Universite Paris Saclay
摘要：We consider the standard site percolation model on the d-dimensional lattice. A direct consequence of the proof of the uniqueness of the infinite cluster of Aizenman, Kesten and Newman [Comm. Math. Phys. 111 (1987) 505-531] is that the two-arms exponent is larger than or equal to 1/2. We improve slightly this lower bound in any dimension d >= 2. Next, starting only with the hypothesis that theta(p) > 0, without using the slab technology, we derive a quantitative estimate establishing long-rang...
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作者：Pinelis, Iosif
作者单位：Michigan Technological University
摘要：It is shown that, for any given p >= 5, A > 0 and B > 0, the exact upper bound on is an element of vertical bar Sigma X-i vertical bar(p) over all independent zero-mean random variables (r.v.'s) X-1, ..., X-n such that Sigma is an element of X-i(2) = B and Sigma is an element of vertical bar X-i vertical bar(p) = A equals c(p) is an element of vertical bar Pi(lambda) - lambda vertical bar(p), where (lambda, c) is an element of (0, infinity)(2) is the unique solution to the system of equations ...
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作者：Roeckner, Michael; Zhu, Rongchan; Zhu, Xiangchan
作者单位：University of Bielefeld; Beijing Institute of Technology; Beijing Jiaotong University
摘要：In this paper, we study the 2D stochastic quasi-geostrophic equation on T-2 for general parameter alpha epsilon (0, 1) and multiplicative noise. We prove the existence of weak solutions and Markov selections for multiplicative noise for all alpha epsilon (0, 1). In the subcritical case alpha > 1/2, we prove existence and uniqueness of (probabilistically) strong solutions. Moreover, we prove ergodicity for the solution of the stochastic quasi-geostrophic equations in the subcritical case driven...
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作者：Lyons, Russell; Peres, Yuval
作者单位：Indiana University System; Indiana University Bloomington; Microsoft
摘要：We introduce a technique using nonbacktracking random walk for estimating the spectral radius of simple random walk. This technique relates the density of nontrivial cycles in simple random walk to that in nonbacktracking random walk. We apply this to infinite Ramanujan graphs, which are regular graphs whose spectral radius equals that of the tree of the same degree. Kesten showed that the only infinite Ramanujan graphs that are Cayley graphs are trees. This result was extended to unimodular r...
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作者：Lawler, Gregory F.; Rezaei, Mohammad A.
作者单位：University of Chicago
摘要：We prove the existence and nontriviality of the d-dimensional 4 Minkowski content for the Schramm-Loewner evolution (SLE kappa) with kappa < 8 and d = 1 + kappa/8 We show that this is a multiple of the natural parameterization.
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作者：Bolthausen, Erwin; den Hollander, Frank; Opoku, Alex A.
作者单位：University of Zurich; Leiden University; Leiden University - Excl LUMC; Delft University of Technology
摘要：In this paper, we consider a random copolymer near a selective interface separating two solvents. The configurations of the copolymer are directed paths that can make i.i.d. excursions of finite length above and below the interface. The excursion length distribution is assumed to have a tail that is logarithmically equivalent to a power law with exponent alpha >= 1. The monomers carry i.i.d. real-valued types whose distribution is assumed to have zero mean, unit variance, and a finite moment g...
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作者：Norris, James; Turner, Amanda
作者单位：University of Cambridge; Lancaster University
摘要：We define a new state-space for the coalescing Brownian flow, also known as the Brownian web, on the circle. The elements of this space are families of order-preserving maps of the circle, depending continuously on two time parameters and having a certain weak flow property. The space is equipped with a complete separable metric. A larger state-space, allowing jumps in time, is also introduced, and equipped with a Skorokhod-type metric, also complete and separable. We prove that the coalescing...
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作者：Bouchard, Bruno; Elie, Romuald; Reveillac, Antony
作者单位：Universite PSL; Universite Paris-Dauphine; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Institut Polytechnique de Paris; ENSAE Paris
摘要：We introduce a new class of backward stochastic differential equations in which the T-terminal value Y-T of the solution (Y, Z) is not fixed as a random variable, but only satisfies a weak constraint of the form E[Psi(Y-T)] >= m, for some (possibly random) nondecreasing map Psi and some threshold m. We name them BSDEs with weak terminal condition and obtain a representation of the minimal time t-values Y-t such that (Y, Z) is a supersolution of the BSDE with weak terminal condition. It provide...
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作者：Hairer, Martin; Hutzenthaler, Martin; Jentzen, Arnulf
作者单位：University of Warwick; Goethe University Frankfurt; Swiss Federal Institutes of Technology Domain; ETH Zurich; Princeton University
摘要：The celebrated Hormander condition is a sufficient (and nearly necessary) condition for a second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficients to be hypoelliptic. As a consequence, the solutions of Kolmogorov PDEs are smooth at all positive times if the coefficients of the PDE are smooth and satisfy Hormander's condition even if the initial function is only continuous but not differentiable. First-order linear Kolmogorov PDEs with smooth coefficients do n...
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作者：Eckhoff, Maren; Kyprianou, Andreas E.; Winkel, Matthias
作者单位：University of Bath; University of Oxford
摘要：Consider a supercritical superdiffusion (X-t)(t >= 0) on a domain D subset of R-d with branching mechanism (x, z) bar right arrow -beta(x)z + alpha(x)z(2) + integral((0, infinity))(e(-zy) - 1 + zy)Pi(x, dy). The skeleton decomposition provides a pathwise description of the process in terms of immigration along a branching particle diffusion. We use this decomposition to derive the strong law of large numbers (SLLN) for a wide class of superdiffusions from the corresponding result for branching...
