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作者：Tsatsoulis, Pavlos; Weber, Hendrik
作者单位：Max Planck Society; University of Bath
摘要：We prove an asymptotic coupling theorem for the 2-dimensional Allen-Cahn equation perturbed by a small space-time white noise. We show that with overwhelming probability two profiles that start close to the minimisers of the potential of the deterministic system contract exponentially fast in a suitable topology. In the 1-dimensional case a similar result was shown in Martinelli et al. (Commun Math Phys 120(1):25-69, 1988; J Stat Phys 55(3-4):477-504, 1989). It is well-known that in two or mor...
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作者：Schoug, Lukas
作者单位：University of Cambridge
摘要：We study SLE kappa (rho) curves, with kappa and rho chosen so that the curves hit the boundary. More precisely, we study the sets on which the curves collide with the boundary at a prescribed angle and determine the almost sure Hausdorff dimensions of these sets. This is done by studying the moments of the spatial derivatives of the conformal maps g(t), by employing the Girsanov theorem and using imaginary geometry techniques to derive a correlation estimate.
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作者：Berestycki, Nathanael; Powell, Ellen; Ray, Gourab
作者单位：University of Vienna; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Victoria
摘要：We prove that a random distribution in two dimensions which is conformally invariant and satisfies a natural domain Markov property is a multiple of the Gaussian free field. This result holds subject only to a fourth moment assumption.
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作者：Dubedat, Julien; Falconet, Hugo
作者单位：Columbia University
摘要：We study the Liouville metric associated to an approximation of a log-correlated Gaussian field with short range correlation. We show that below a parameter gamma(c) > 0, the left-right length of rectangles for the Riemannian metric e(gamma phi 0,n)ds(2) with various aspect ratio is concentrated with quasi-lognormal tails, that the renormalized metric is tight when gamma < min(gamma(c), 0.4) and that subsequential limits are consistent with the Weyl scaling.
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作者：Holden, Nina; Sheffield, Scott
作者单位：Massachusetts Institute of Technology (MIT)
摘要：The Schelling model of segregation, introduced by Schelling in 1969 as a model for residential segregation in cities, describes how populations of multiple types self-organize to form homogeneous clusters of one type. In this model, vertices in an N-dimensional lattice are initially assigned types randomly. As time evolves, the type at a vertex v has a tendency to be replaced with the most common type within distance w of v. We present the first mathematical description of the dynamical scalin...
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作者：Chevyrev, Ilya; Friz, Peter K.; Korepanov, Alexey; Melbourne, Ian
作者单位：University of Edinburgh; Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Exeter; University of Warwick
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作者：Han, Yanjun; Jiao, Jiantao; Mukherjee, Rajarshi
作者单位：Stanford University; University of California System; University of California Berkeley; Harvard University; Harvard T.H. Chan School of Public Health
摘要：We provide a complete picture of asymptotically minimax estimation of L-r-norms (for any r >= 1) of the mean in Gaussian white noise model over Nikolskii-Besov spaces. In this regard, we complement the work of Lepski et al. (Probab Theory Relat Fields 113(2):221-253, 1999), who considered the cases of r = 1 (with poly-logarithmic gap between upper and lower bounds) and r even (with asymptotically sharp upper and lower bounds) over Holder spaces. We additionally consider the case of asymptotica...
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作者：Eskenazis, Alexandros; Ivanisvili, Paata
作者单位：Princeton University; University of California System; University of California Irvine; Sorbonne Universite; Universite Paris Cite
摘要：Let (X, parallel to . parallel to(X)) be a Banach space. The purpose of this article is to systematically investigate dimension independent properties of vector valued functions f : {-1, 1}(n) -> X on the Hamming cube whose spectrum is bounded above or below. Our proofs exploit contractivity properties of the heat flow, induced by the geometry of the target space (X, parallel to . parallel to (X)), combined with duality arguments and suitable tools from approximation theory and complex analysi...
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作者：Zhang, Deng
作者单位：Shanghai Jiao Tong University
摘要：We study optimal control problems for stochastic nonlinear Schrodinger equations in both the mass subcritical and critical case. For general initial data of the minimal L-2 regularity, we prove the existence and first order Lagrange condition of an open loop control. In particular, these results apply to the stochastic nonlinear Schrodinger equations with the critical quintic and cubic nonlinearities in dimensions one and two, respectively. Furthermore, we obtain uniform estimates of (backward...
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作者：Lyons, Russell; White, Graham
作者单位：Indiana University System; Indiana University Bloomington
摘要：Dyadic lattice graphs and their duals are commonly used as discrete approximations to the hyperbolic plane. We use them to give examples of random rooted graphs that are stationary for simple random walk, but whose duals have only a singular stationary measure. This answers a question of Curien and shows behaviour different from the unimodular case. The consequence is that planar duality does not combine well with stationary random graphs. We also study harmonic measure on dyadic lattice graph...
