-
作者：Bedrossian, Jacob; Blumenthal, Alex; Punshon-Smith, Sam
作者单位：University System of Maryland; University of Maryland College Park; University System of Georgia; Georgia Institute of Technology; Brown University
摘要：We study the mixing and dissipation properties of the advection-diffusion equation with diffusivity 0 < kappa << 1 and advection by a class of random velocity fields on T-d, d = {2, 3}, including solutions of the 2D Navier-Stokes equations forced by sufficiently regular-in-space, non-degenerate white-in-time noise. We prove that the solution almost surelymixes exponentially fast uniformly in the diffusivity kappa. Namely, that there is a deterministic, exponential rate (independent of kappa) s...
-
作者：Baraud, Yannick
作者单位：University of Luxembourg
摘要：We consider the problem of estimating the joint distribution of n independent random variables. Given a loss function and a family of candidate probabilities, that we shall call a model, we aim at designing an estimator with values in our model that possesses good estimation properties not only when the distribution of the data belongs to the model but also when it lies close enough to it. The losses we have in mind are the total variation, Hellinger, Wasserstein and L-p-distances to name a fe...
-
作者：Banerjee, Sayan; Bhamidi, Shankar
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We consider models of evolving networks (G(n) : n >= 0) modulated by two parameters: an attachment function f : N-0 -> R+ and a (possibly random) attachment sequence (mi : i >= 1). Starting with a single vertex, at each discrete step i >= 1 a new vertex vi enters the system with m(i) >= 1 edges which it sequentially connects to a preexisting vertex v is an element of G(i-1) with probability proportional to f (degree(v)). We consider the problem of emergence of persistent hubs: existence of a f...
-
作者：Troscheit, Sascha
作者单位：University of Vienna
摘要：The Brownian map is a model of random geometry on the sphere and as such an important object in probability theory and physics. It has been linked to Liouville Quantum Gravity and much research has been devoted to it. One open question asks for a canonical embedding of the Brownian map into the sphere or other, more abstract, metric spaces. Similarly, Liouville Quantum Gravity has been shown to be equivalent to the Brownian map but the exact nature of the correspondence (i.e. embedding) is sti...
-
作者：Miller, Jason; Sheffield, Scott
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：Previous works in this series have shown that an instance of a root 8/3-Liouville quantum gravity (LQG) sphere has a well-defined distance function, and that the resulting metric measure space (mm-space) agrees in law with the Brownian map (TBM). In this work, we show that given just the mm-space structure, one can a.s. recover the LQG sphere. This implies that there is a canonical way to parameterize an instance of TBM by the Euclidean sphere (up to Mobius transformation). In other words, an ...
-
作者：Addario-Berry, Louigi; Sen, Sanchayan
作者单位：McGill University; Indian Institute of Science (IISC) - Bangalore
摘要：The global structure of the minimal spanning tree (MST) is expected to be universal for a large class of underlying random discrete structures. However, very little is known about the intrinsic geometry of MSTs of most standard models, and so far the scaling limit of the MST viewed as a metric measure space has only been identified in the case of the complete graph (Addario-Berry et al. in Ann Probab 45(5):3075-3144, 2017). In this work, we show that the MST constructed by assigning i.i.d. con...
-
作者：Baik, Jinho; Liu, Zhipeng
作者单位：University of Michigan System; University of Michigan; University of Kansas
摘要：We consider the one-dimensional totally asymmetric simple exclusion process with an arbitrary initial condition in a spatially periodic domain, and obtain explicit formulas for the multi-point distributions in the space-time plane. The formulas are given in terms of an integral involving a Fredholm determinant. We then evaluate the large-time, large-period limit in the relaxation time scale, which is the scale such that the system size starts to affect the height fluctuations. The limit is obt...
-
作者：Chapon, Francois; Chhaibi, Reda
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：The classical theorem by Pitman states that a Brownianmotionminus twice its running infimum enjoys the Markov property. On the one hand, Biane understood that Pitman's theorem is intimately related to the representation theory of the quantum group U-q (sl(2)), in the so-called crystal regime q -> 0. On the other hand, Bougerol and Jeulin showed the appearance of exactly the same Pitman transform in the infinite curvature limit r. 8 of a Brownian motion on the hyperbolic space H-3 = SL2(C)/SU2....
-
作者：Buchholz, Simon
作者单位：University of Bonn
摘要：We consider gradient fields on Z(d) for potentials V that can be expressed as e(-V(x)) = pe -qx(2)/2 + (1 - p)e-x(2)/2. This representation allows us to associate a random conductance type model to the gradient fields with zero tilt. We investigate this random conductance model and prove correlation inequalities, duality properties, and uniqueness of the Gibbs measure in certain regimes. We then show that there is a close relation between Gibbs measures of the random conductance model and grad...
-
作者：[Anonymous]
