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作者：Benoist, Stephane; Dumaz, Laure; Werner, Wendelin
作者单位：Massachusetts Institute of Technology (MIT); Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study random two-dimensional spanning forests in the plane that can be viewed both in the discrete case and in their appropriately taken scaling limits as a uniformly chosen spanning tree with some Poissonian deletion of edges or points. We show how to relate these scaling limits to a stationary distribution of a natural coalescent-type Markov process on a state space of abstract graphs with real-valued edge weights. This Markov process can be interpreted as a renormalization flow. This pro...
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作者：Gerstenberg, Julian
作者单位：Leibniz University Hannover
摘要：A hypergraph (V, E) is called an interval hypergraph if there exists a linear order l on V such that every edge e is an element of E is an interval w.r.t. l; we also assume that {j} is an element of E for every j is an element of V. Our main result is a de Finetti-type representation of random exchangeable interval hypergraphs on N (EIHs): the law of every EIH can be obtained by sampling from some random compact subset K of the triangle {(x, y) : 0 <= x <= y <= 1} at i.i.d. uniform positions U...
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作者：Sabot, Christophe; Zeng, Xiaolin
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：Consider a negatively drifted one-dimensional Brownian motion starting at positive initial position, its first hitting time to 0 has the inverse Gaussian law. Moreover, conditionally on this hitting time, the Brownian motion up to that time has the law of a three-dimensional Bessel bridge. In this paper, we give a generalization of this result to a family of Brownian motions with interacting drifts, indexed by the vertices of a conductance network. The hitting times are equal in law to the inv...
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作者：Delarue, Francois; Lacker, Daniel; Ramanan, Kavita
作者单位：Universite Cote d'Azur; Columbia University; Brown University
摘要：We study a sequence of symmetric n-player stochastic differential games driven by both idiosyncratic and common sources of noise, in which players interact with each other through their empirical distribution. The unique Nash equilibrium empirical measure of the n-player game is known to converge, as n goes to infinity, to the unique equilibrium of an associated mean field game. Under suitable regularity conditions, in the absence of common noise, we complement this law of large numbers result...
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作者：Bender, Christian
作者单位：Saarland University
摘要：We introduce a Skorokhod type integral and prove an Ito formula for a wide class of Gaussian processes which may exhibit stochastic discontinuities. Our Ito formula unifies and extends the classical one for general (i.e., possibly discontinuous) Gaussian martingales in the sense of Ito integration and the one for stochastically continuous Gaussian non-martingales in the Skorokhod sense, which was first derived in Ales et al.
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作者：Aimino, Romain; Liverani, Carlangelo
作者单位：Universidade do Porto; University of Rome Tor Vergata
摘要：Motivated by the random Lorentz gas, we study deterministic walks in random environment and show that (in simple, yet relevant cases) they can be reduced to a class of random walks in random environment where the jump probability depends (weakly) on the past. In addition, we prove few basic results (hopefully, the germ of a general theory) for the latter purely probabilistic model.
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作者：Carmona, Rene; Delarue, Francois; Lacker, Daniel
作者单位：Princeton University; Universite Cote d'Azur; Columbia University
摘要：This note corrects an error in [1], Lemma 3.7. The lemma is not correct as stated, and the first conclusion must instead be stated as a hypothesis. This erratum corrects the statement of the lemma and then shows that the additional hypothesis is satisfied in each of the three applications of the lemma later in the paper. The main results of the paper remain unchanged. The error in [1], Lemma 3.7, is at the end of the first step of the proof. Specifically, the last equation before the second st...
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作者：Gwynne, Ewain; Miller, Jason
作者单位：University of Cambridge
摘要：We prove that for any metric, which one can associate with a Liouville quantum gravity (LQG) surface for gamma is an element of (0, 2) satisfying certain natural axioms, its geodesics exhibit the following confluence property. For any fixed point z, a.s. any two gamma-LQG geodesics started from distinct points other than z must merge into each other and subsequently coincide until they reach z. This is analogous to the confluence of geodesics property for the Brownian map proven by Le Gall (Ac...
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作者：Ding, Jian; Wirth, Mateo
作者单位：University of Pennsylvania
摘要：We study level-set percolation for Gaussian free fields on metric graphs. In two dimensions, we give an upper bound on the chemical distance between the two boundaries of a macroscopic annulus. Our bound holds with high probability conditioned on connectivity and is sharp up to a poly-logarithmic factor with an exponent of one-quarter. This substantially improves a previous result by Li and the first author. In three dimensions and higher, we provide rather precise estimates of percolation pro...
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作者：Asselah, Amine; Schapira, Bruno
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Aix-Marseille Universite
摘要：We study scenarii linked with the Swiss cheese picture in dimension 3 obtained when two random walks are forced to meet often, or when one random walk is forced to squeeze its range. In the case of two random walks, we show that they most likely meet in a region of optimal density. In the case of one random walk, we show that a small range is reached by a strategy uniform in time. Both results rely on an original inequality estimating the cost of visiting sparse sites, and in the case of one r...
