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作者：Brito, Gerandy; Damron, Michael; Hanson, Jack
作者单位：University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology; City University of New York (CUNY) System; City College of New York (CUNY)
摘要：In first-passage percolation (FPP), one places nonnegative random vari-ables (weights) (te) on the edges of a graph and studies the induced weighted graph metric. We consider FPP on Zd for d > 2 and analyze the geometric properties of geodesics, which are optimizing paths for the metric. Specifi-cally, we address the question of existence of bigeodesics, which are doubly-infinite paths whose subpaths are geodesics. It is a famous conjecture origi-nating from a question of Furstenberg and most ...
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作者：Contat, Alice; Curien, Nicolas
作者单位：Universite Paris Saclay
摘要：Consider a uniform rooted Cayley tree T-n with n vertices and let m cars arrive sequentially, independently, and uniformly on its vertices. Each car tries to park on its arrival node, and if the spot is already occupied, it drives towards the root of the tree and parks as soon as possible. Lackner and Panholzer (J. Combin. Theory Ser. A 142 (2016) 1-28) established a phase transition for this process when m approximate to n/2. In this work, we couple this model with a variant of the classical ...
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作者：Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider Ito uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in W12+epsilon,loc, and the drift in a Morrey class containing Ld. We prove the unique strong solvability in the class of admissible solutions for any starting point. The result is new even if the diffusion is constant.
