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作者：Durrett, Rick; Remenik, Daniel
作者单位：Duke University; University of Toronto
摘要：We consider a branching-selection system in R with N particles which give birth independently at rate 1 and where after each birth the leftmost particle is erased, keeping the number of particles constant. We show that, as N -> 8, the empirical measure process associated to the system converges in distribution to a deterministic measure-valued process whose densities solve a free boundary integro-differential equation. We also show that this equation has a unique traveling wave solution travel...
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作者：Kenyon, Richard
作者单位：Brown University
摘要：The classical matrix-tree theorem relates the determinant of the combinatorial Laplacian on a graph to the number of spanning trees. We generalize this result to Laplacians on one- and two-dimensional vector bundles, giving a combinatorial interpretation of their determinants in terms of so-called cycle rooted spanning forests (CRSFs). We construct natural measures on CRSFs for which the edges form a determinantal process. This theory gives a natural generalization of the spanning tree process...
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作者：Dekking, Michel; Simon, Karoly; Szekely, Balazs
作者单位：Delft University of Technology; Budapest University of Technology & Economics
摘要：In this paper, we consider a family of random Cantor sets on the line and consider the question of whether the condition that the sum of the Hausdorff dimensions is larger than one implies the existence of interior points in the difference set of two independent copies. We give a new and complete proof that this is the case for the random Cantor sets introduced by Per Larsson.
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作者：Gozlan, Nathael; Roberto, Cyril; Samson, Paul-Marie
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We show that Talaurand's transport inequality is equivalent to a restricted logarithmic Sobolev inequality. This result clarifies the links between these two important functional inequalities. As an application, we give the first proof of the fact that Talagrand's inequality is stable under bounded perturbations.
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作者：Cerrai, Sandra; Freidlin, Mark
作者单位：University System of Maryland; University of Maryland College Park
摘要：We consider a class of stochastic reaction-diffusion equations also having a stochastic perturbation on the boundary and we show that when the diffusion rate is much larger than the rate of reaction, it is possible to replace the SPDE by a suitable one-dimensional stochastic differential equation. This replacement is possible under the assumption of spectral gap for the diffusion and is a result of averaging in the fast spatial transport. We also study the fluctuations around the averaged moti...
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作者：Crane, Edward; Georgiou, Nicholas; Volkov, Stanislav; Wade, Andrew R.; Waters, Robert J.
作者单位：University of Bristol; University of Strathclyde
摘要：We study a generalized Polya urn model with two types of ball. If the drawn ball is red, it is replaced together with a black ball, but if the drawn ball is black it is replaced and a red ball is thrown out of the urn. When only black balls remain, the roles of the colors are swapped and the process restarts. We prove that the resulting Markov chain is transient but that if we throw out a ball every time the colors swap, the process is recurrent. We show that the embedded process obtained by o...
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作者：Zhang, Tusheng
作者单位：University of Manchester
摘要：In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order elliptic partial differential equations. Our approach is probabilistic. The theory of Dirichlet processes and backward stochastic differential equations play a crucial role.
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作者：Mendelson, Shahar
作者单位：Technion Israel Institute of Technology; Australian National University
摘要：We show that for a typical coordinate projection of a subgaussian class of functions, the infimum over signs inf((epsilon i)) sup f epsilon F |Sigma(k)(i)=1 epsilon(i) f (X-i)| is asymptotically smaller than the expectation over signs as a function of the dimension k, if the canonical Gaussian process indexed by F is continuous. To that end, we establish a bound on the discrepancy of an arbitrary subset of R-k using properties of the canonical Gaussian process the set indexes, and then obtain ...
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作者：Blath, Jochen; Doering, Leif; Etheridge, Alison
作者单位：Technical University of Berlin; University of Oxford
摘要：In this paper we introduce a critical curve separating the asymptotic behavior of the moments of the symbiotic branching model, introduced by Etheridge and Fleischmann [Stochastic Process. Appl. 114 (2004) 127-160] into two regimes. Using arguments based on two different dualities and a classical result of Spitzer [Trans. Amer Math. Soc. 87 (1958) 187-197] on the exit-time of a planar Brownian motion from a wedge, we prove that the parameter governing the model provides regimes of bounded and ...
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作者：Hu, Yaozhong; Nualart, David; Song, Jian
作者单位：University of Kansas
摘要：We establish a version of the Feynman-Kac formula for the multidimensional stochastic heat equation with a multiplicative fractional Brownian sheet. We use the techniques of Malliavin calculus to prove that the process defined by the Feynman-Kac formula is a weak solution of the stochastic heat equation. From the Feynman-Kac formula, we establish the smoothness of the density of the solution and the Holder regularity in the space and time variables. We also derive a Feynman-Kac formula for the...
