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作者：Kenyon, Richard
作者单位：Brown University
摘要：We generalize the uniform spanning tree to construct a family of determinantal measures on essential spanning forests on periodic planar graphs in which every component tree is bi-infinite. Like the uniform spanning tree, these measures arise naturally from the Laplacian on the graph. More generally, these results hold for the massive Laplacian determinant which counts rooted spanning forests with weight M per finite component. These measures typically have a form of conformal invariance, unli...
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作者：Defosseux, Manon
作者单位：Universite Paris Cite
摘要：We consider the coadjoint action of a Loop group of a compact group on the dual of the corresponding centrally extended Loop algebra and prove that a Brownian motion in a Cartan subalgebra conditioned to remain in an affine Weyl chamber-which can be seen as a space time conditioned Brownian motion-is distributed as the radial part process of a Brownian sheet on the underlying Lie algebra.
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作者：Dembo, Amir; Levit, Anna; Vadlamani, Sreekar
作者单位：Stanford University; Stanford University; University of British Columbia; Tata Institute of Fundamental Research (TIFR); TIFR Centre for Applicable Mathematics (CAM), Bengaluru
摘要：The N vertices of a quantum random graph are each a circle independently punctured at Poisson points of arrivals, with parallel connections derived through for each pair of these punctured circles by yet another independent Poisson process. Considering these graphs at their critical parameters, we show that the joint law of the rescaled by N-2/3 and ordered sizes of their connected components, converges to that of the ordered lengths of excursions above zero for a reflected Brownian motion wit...
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作者：Feng, Renjie; Adler, Robert J.
作者单位：Peking University; Technion Israel Institute of Technology
摘要：We first consider deterministic immersions of the d-dimensional sphere into high dimensional Euclidean spaces, where the immersion is via spherical harmonics of level n. The main result of the article is the, a priori unexpected, fact that there is a uniform lower bound to the critical radius of the immersions as n -> infinity. This fact has immediate implications for random spherical harmonics with fixed L-2 -norm. In particular, it leads to an exact and explicit formulae for the tail probabi...
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作者：Furlan, Marco; Gubinelli, Massimiliano
作者单位：Universite PSL; Universite Paris-Dauphine; University of Bonn
摘要：We introduce a nonlinear paracontrolled calculus and use it to renor- malise a class of singular SPDEs including certain quasilinear variants of the periodic two-dimensional parabolic Anderson model.
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作者：del Barrio, Eustasio; Loubes, Jean-Michel
作者单位：Universidad de Valladolid; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on R-d, with d >= 1. We provide new results on the uniqueness and stability of the associated optimal transportation potentials, namely, the minimizers in the dual formulation of the optimal transportation problem. As a consequence, we show that a CLT holds for the empirical transportation cost under mild moment and smoothness requirements. The limiting distributio...
