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作者：Toth, Balint
作者单位：University of Bristol; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences
摘要：We prove the quenched version of the central limit theorem for the displacement of a random walk in doubly stochastic random environment, under the H-1-condition, with slightly stronger, L2+epsilon (rather than L-2) integrability condition on the stream tensor. On the way we extend Nash's moment bound to the nonreversible, divergence-free drift case, with unbounded (L2+epsilon) stream tensor. This paper is a sequel of [Ann. Probab. 45 (2017) 4307-4347] and relies on technical results quoted fr...
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作者：Hairer, M.; Matetski, K.
作者单位：Imperial College London; University of Toronto
摘要：We develop a general framework for spatial discretisations of parabolic stochastic PDEs whose solutions are provided in the framework of the theory of regularity structures and which are functions in time. As an application, we show that the dynamical Phi(4)(3) model on the dyadic grid converges after renormalisation to its continuous counterpart. This result in particular implies that, as expected, the Phi(4)(3) measure with a sufficiently small coupling constant is invariant for this equatio...
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作者：Kraaij, Richard C.
作者单位：Ruhr University Bochum
摘要：We study the large deviation behaviour of the trajectories of empirical distributions of independent copies of time-homogeneous Feller processes on locally compact metric spaces. Under the condition that we can find a suitable core for the generator of the Feller process, we are able to define a notion of absolutely continuous trajectories of measures in terms of some topology on this core. Also, we define a Hamiltonian in terms of the linear generator and a Lagrangian as its Legendre transfor...
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作者：Borgs, Christian; Chayes, Jennifer T.; Cohn, Henry; Zhao, Yufei
作者单位：Microsoft; Massachusetts Institute of Technology (MIT)
摘要：We extend the L-p theory of sparse graph limits, which was introduced in a companion paper, by analyzing different notions of convergence. Under suitable restrictions on node weights, we prove the equivalence of metric convergence, quotient convergence, microcanonical ground state energy convergence, microcanonical free energy convergence and large deviation convergence. Our theorems extend the broad applicability of dense graph convergence to all sparse graphs with unbounded average degree, w...
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作者：Eskenazis, Alexandros; Nayar, Piotr; Tkocz, Tomasz
作者单位：Princeton University; University of Warsaw
摘要：A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures include random variables with densities proportional to e(-vertical bar t vertical bar P )and symmetric p-stable random variables, where p is an element of (0, 2]. We obtain various sharp moment and entropy comparison estimates for weighted sums of independ...
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作者：Gladkich, Alexey; Peled, Ron
作者单位：Tel Aviv University
摘要：We study the length of cycles of random permutations drawn from the Mallows distribution. Under this distribution, the probability of a permutation pi is an element of S-n is proportional to q(inv(pi)) where q > 0 and inv(pi) is the number of inversions in pi. We focus on the case that q < 1 and show that the expected length of the cycle containing a given point is of order min{(1 - q)(-2), n}. This marks the existence of two asymptotic regimes: with high probability, when n tends to infinity ...
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作者：Hammond, Alan
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：For d >= 2 and n is an element of N even, let p(n) = p(n)(d) denote the number of length n self-avoiding polygons in Z(d) up to translation. The polygon cardinality grows exponentially, and the growth rate lim(n is an element of 2N) (1/n)(pn) is an element of (0,infinity) is called the connective constant and denoted by mu. Madras [J. Stat. Phys. 78 (1995) 681-699] has shown that p(n)mu(-n) <= Cn(-1/2) in dimension d = 2. Here, we establish that p(n)mu(-n) <= n(-3/2+o(1)) for a set of even n o...
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作者：Baik, Jinho; Barraquand, Guillaume; Corwin, Ivan; Suidan, Toufic
作者单位：University of Michigan System; University of Michigan; Columbia University
摘要：We study last passage percolation in a half-quadrant, which we analyze within the framework of Pfaffian Schur processes. For the model with exponential weights, we prove that the fluctuations of the last passage time to a point on the diagonal are either GSE Tracy-Widom distributed, GOE Tracy- Widom distributed or Gaussian, depending on the size of weights along the diagonal. Away from the diagonal, the fluctuations of passage times follow the GUE Tracy-Widom distribution. We also obtain a two...
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作者：Denisov, Denis; Sakhanenko, Alexander; Wachtel, Vitali
作者单位：University of Manchester; Nankai University; University of Augsburg
摘要：We consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first passage times over moving boundaries. Furthermore, we prove that a properly rescaled random walk conditioned to stay above the boundary up to time n converges, as n -> infinity towards the Brownian meander.
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作者：Bertoin, Jean; Curien, Nicolas; Kortchemski, Igor
作者单位：University of Zurich; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We are interested in the cycles obtained by slicing at all heights random Boltzmann triangulations with a simple boundary. We establish a functional invariance principle for the lengths of these cycles, appropriately rescaled, as the size of the boundary grows. The limiting process is described using a self-similar growth-fragmentation process with explicit parameters. To this end, we introduce a branching peeling exploration of Boltzmann triangulations, which allows us to identify a crucial m...
