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作者：Saloff-Coste, Laurent; Zheng, Tianyi
作者单位：Cornell University; University of California System; University of California San Diego
摘要：We study the isoperimetric and spectral profiles of certain families of finitely generated groups defined via actions on labelled Schreier graphs and simple gluing of such. In one of our simplest constructions-the pocket-extension of a group G-this leads to the study of certain finitely generated subgroups of the full permutation group S(G boolean OR{*}). Some sharp estimates are obtained while many challenging questions remain.
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作者：Balazs, Marton; Busani, Ofer; Seppalainen, Timo
作者单位：University of Bristol; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider point-to-point last-passage times to every vertex in a neighbourhood of size delta N-2/3 at distance N from the starting point. The increments of the last-passage times in this neighbourhood are shown to be jointly equal to their stationary versions with high probability that depends only on delta. Through this result we show that (1) the Airy(2) process is locally close to a Brownian motion in total variation; (2) the tree of point-to-point geodesics from every vertex in a box of ...
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作者：Broutin, Nicolas; Duquesne, Thomas; Wang, Minmin
作者单位：Sorbonne Universite; University of Sussex
摘要：We consider a natural model of inhomogeneous random graphs that extends the classical Erdos-Renyi graphs and shares a close connection with the multiplicative coalescence, as pointed out by Aldous (Ann Probab 25:812-854, 1997). In this model, the vertices are assigned weights that govern their tendency to form edges. It is by looking at the asymptotic distributions of the masses (sum of the weights) of the connected components of these graphs that Aldous and Limic (Electron J Probab 3:1-59, 19...
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作者：Lees, Benjamin; Taggi, Lorenzo
作者单位：University of Bristol; University of Bristol; Sapienza University Rome
摘要：We prove exponential decay of transverse correlations in the Spin O(N) model for arbitrary non-zero values of the external magnetic field and arbitrary spin dimension N > 1. Our result is new when N > 3, in which case no Lee-Yang theorem is available, it is an alternative to Lee-Yang when N = 2, 3, and also holds for a wide class of multi-component spin systems with continuous symmetry. The key ingredients are a representation of the model as a system of coloured random paths, a 'colour-switch...
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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...
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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...
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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...
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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...
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作者：Le Gall, Jean-Francois; Riera, Armand
作者单位：Universite Paris Cite
摘要：We provide a unified approach to the three main non-compact models of random geometry, namely the Brownian plane, the infinite-volume Brownian disk, and the Brownian half-plane. This approach allows us to investigate relations between these models, and in particular to prove that complements of hulls in the Brownian plane are infinite-volume Brownian disks.
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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 ...
