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作者：Hairer, Martin; Li, Xue-Mei
作者单位：Imperial College London
摘要：We consider slow/fast systems where the slow system is driven by fractional Brownian motion with Hurst parameter H > 1/2. We show that unlike in the case H = 1/2, convergence to the averaged solution takes place in probability and the limiting process solves the 'naively' averaged equation. Our proof strongly relies on the recently obtained stochastic sewing lemma.
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作者：Kosloff, Zemer; Soo, Terry
作者单位：Hebrew University of Jerusalem; University of London; University College London
摘要：Ornstein and Shields (Advances in Math. 10 (1973) 143-146) proved that Brownian motion reflected on a bounded region is an infinite entropy Bernoulli flow, and, thus, Ornstein theory yielded the existence of a measure-preserving isomorphism between any two such Brownian motions. For fixed h > 0, we construct by elementary methods, isomorphisms with almost surely finite coding windows between Brownian motions reflected on the intervals [0, qh] for all positive rationals q.
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作者：Spinka, Yinon
作者单位：University of British Columbia
摘要：We show that any finitely dependent invariant process on a transitive amenable graph is a finitary factor of an i.i.d. process. With an additional assumption on the geometry of the graph, namely that no two balls with different centers are identical, we further show that the i.i.d. process may be taken to have entropy arbitrarily close to that of the finitely dependent process. As an application, we give an affirmative answer to a question of Holroyd (Ann. Inst. Henri Poincare Probab. Stat. 53...
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作者：Bella, Peter; Schaffner, Mathias
作者单位：Dortmund University of Technology; Leipzig University
摘要：We consider the random conductance model in a stationary and ergodic environment. Under suitable moment conditions on the conductances and their inverse, we prove a quenched invariance principle for the random walk among the random conductances. The moment conditions improve earlier results of Andres, Deuschel and Slowik (Ann. Probab. 43 (2015) 1866-1891) and are the minimal requirement to ensure that the corrector is sublinear everywhere. The key ingredient is an essentially optimal determini...
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作者：Schapira, Bruno
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a central limit theorem for the capacity of the range of a symmetric random walk on Z(5) , under only a moment condition on the step distribution. The result is analogous to the central limit theorem for the size of the range in dimension three, obtained by Jain and Pruitt in 1971. In particular, an atypical logarithmic correction appears in the scaling of the variance. The proof is based on new asymptotic estimates, which hold in any dimension d >= 5, for the probability that the ran...
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作者：Eldan, Ronen; Mikulincer, Dan; Zhai, Alex
作者单位：Weizmann Institute of Science; Stanford University
摘要：We introduce a new method for obtaining quantitative convergence rates for the central limit theorem (CLT) in a high-dimensional setting. Using our method, we obtain several new bounds for convergence in transportation distance and entropy, and in particular: (a) We improve the best known bound, obtained by the third named author (Probab. Theory Related Fields 170 (2018) 821-845), for convergence in quadratic Wasserstein transportation distance for bounded random vectors; (b) we derive the fir...
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作者：Gwynne, Ewain; Holden, Nina; Miller, Jason
作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The peanosphere construction of Duplantier, Miller and Sheffield provides a means of representing a gamma-Liouville quantum gravity (LQG) surface, gamma is an element of(0, 2), decorated with a space-filling form of Schramm's SLE kappa(,) kappa = 16/gamma(2) is an element of (4, infinity), eta as a gluing of a pair of trees which are encoded by a correlated two-dimensional Brownian motion Z. We prove a KPZ-type formula which relates the Hausdorff dimension of any Borel subset A of the range of...
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作者：Mukherjee, Chiranjib; Varadhan, S. R. S.
作者单位：University of Munster; New York University
摘要：The path measure corresponding to the Frohlich polaron appearing in quantum statistical mechanics is defined as the tilted measure d (P) over cap (epsilon),T = 1/Z(epsilon, T) exp{1/2 integral-(T)(T)integral-(T)(T) epsilon e(-epsilon vertical bar t-s vertical bar)/vertical bar omega(t) - omega(s)vertical bar ds dt}dP. Here, epsilon > 0 is a constant known as the Kac parameter or the inverse-coupling parameter, and P is the distribution of the increments of the three-dimensional Brownian motion...
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作者：Teyssier, Lucas
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：We present an improved version of Diaconis-Shahshahani upper bound lemma, which is used to compute the limiting value of the distance to stationarity. We then apply it to the random transposition shuffle.
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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...
