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作者：Baur, Erich; Miermont, Gregory; Ray, Gourab
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); University of Victoria
摘要：We study noncompact scaling limits of uniform random planar quadran-gulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe different limiting metric spaces. Among well-known objects like the Brownian plane or the self-similar continuum random tree, we construct two new one-parameter families of metric spaces that appear as scaling limits: the Brownian half-plane with skewness parame...
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作者：Hammond, Alan
作者单位：University of California System; University of California Berkeley
摘要：In last passage percolation models lying in the KPZ universality class, the energy of long energy-maximizing paths may be studied as a function of the paths' pair of endpoint locations. Scaled coordinates may be introduced, so that these maximizing paths, or polymers, now cross unit distances with unit-order fluctuations, and have scaled energy, or weight, of unit order. In this article, we consider Brownian last passage percolation in these scaled coordinates. In the narrow wedge case, one en...
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作者：Nam, Danny; Sly, Allan
作者单位：Princeton University
摘要：We study the Swendsen-Wang dynamics for the q-state Potts model on the lattice. Introduced as an alternative algorithm of the classical single-site Glauber dynamics, the Swendsen-Wang dynamics is a nonlocal Markov chain that recolors many vertices at once based on the random-cluster representation of the Potts model. In this work, we establish cutoff phenomenon for the Swendsen-Wang dynamics on the lattice at sufficiently high temperatures, proving that it exhibits a sharp transition from unmi...
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作者：Hairer, Martin; Xu, Weijun
作者单位：Imperial College London; University of Oxford; New York University; NYU Shanghai
摘要：We extend the weak universality of KPZ in [An analytic BPHZ theorem for regularity structures (2016)] to weakly asymmetric interface models with general growth mechanisms beyond polynomials. A key new ingredient is a pointwise bound on correlations of trigonometric functions of Gaussians in terms of their polynomial counterparts. This enables us to reduce the problem of a general nonlinearity with sufficient regularity to that of a polynomial.
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作者：Austin, Tim
作者单位：University of California System; University of California Los Angeles
摘要：Let K-1, ..., K-n, be bounded, complete, separable metric spaces. Let lambda(i) be a Borel probability measure on K-i for each i. Let f : Pi(i) K-i -> R be a bounded and continuous potential function, and let mu(dx) proportional to e(f(x))lambda(1)(dx(1)) ... lambda(n) (dx(n)) be the associated Gibbs distribution. At each point x is an element of Pi(i) K-i, one can define a 'discrete gradient' del f (x, .) by comparing the values of f at all points which differ from x in at most one coordinate...
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作者：Cipriani, Alessandra; Dan, Biltu; Hazra, Rajat Subhra
作者单位：Delft University of Technology; Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：On the integer lattice, we consider the discrete membrane model, a random interface in which the field has Laplacian interaction. We prove that, under appropriate rescaling, the discrete membrane model converges to the continuum membrane model in d >= 2. Namely, it is shown that the scaling limit in d = 2, 3 is a Holder continuous random field, while in d >= 4 the membrane model converges to a random distribution. As a by-product of the proof in d = 2, 3, we obtain the scaling limit of the max...
