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作者：Nam, Kyeongsik
作者单位：University of California System; University of California Berkeley
摘要：We develop a unified theory to analyze the microcanonical ensembles with several constraints given by unbounded observables. Several interesting phenomena that do not occur in the single constraint case can happen under the multiple constraints case. We systematically analyze the detailed structures of such microcanonical ensembles in two orthogonal directions using the theory of large deviations. First of all, we establish the equivalence of ensembles result, which exhibits an interesting pha...
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作者：Angst, Jurgen; Poly, Guillaume
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the absolute continuity with respect to the Lebesgue measure of the distribution of the nodal volume associated with a smooth, nondegencrate and stationary Gaussian field (f (x), x is an element of R-d). Under mild conditions, we prove that in dimension d >= 3, the distribution of the nodal volume has an absolutely continuous component plus a possible singular part. This singular part is actually unavoidable bearing in mind that some Gaussian processes have a positive probability to k...
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作者：Meszaros, Andras
作者单位：Central European University
摘要：We extend Lyons's tree entropy theorem to general determinantal measures. As a byproduct we show that the sofic entropy of an invariant determinantal measure does not depend on the chosen sofic approximation.
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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：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：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：Caputo, Pietro; Labbe, Cyril; Lacoin, Hubert
作者单位：Roma Tre University; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：By viewing the N-simplex as the set of positions of N - 1 ordered particles on the unit interval, the adjacent walk is the continuous-time Markov chain obtained by updating independently at rate 1 the position of each particle with a sample from the uniform distribution over the interval given by the two particles adjacent to it. We determine its spectral gap and prove that both the total variation distance and the separation distance to the uniform distribution exhibit a cutoff phenomenon, wi...
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作者：Duminil-Copin, Hugo; Kesten, Harry; Nazarov, Fedor; Peres, Yuval; Sidoravicius, Vladas
作者单位：University of Geneva; Cornell University; University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent; Microsoft; New York University; NYU Shanghai
摘要：We show that the number of maximal paths in directed last-passage percolation on the hypercubic lattice Z(d) (d >= 2) in which weights take finitely many values is typically exponentially large.
