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作者：Cook, Nicholas A.
作者单位：University of California System; University of California Los Angeles
摘要：We prove that the (non-symmetric) adjacency matrix of a uniform random d-regular directed graph on n vertices is asymptotically almost surely invertible, assuming for a sufficiently large constant . The proof makes use of a coupling of random regular digraphs formed by shuffling the neighborhood of a pair of vertices, as well as concentration results for the distribution of edges, proved in Cook (Random Struct Algorithms. 2014). We also apply our general approach to prove asymptotically almost...
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作者：Klopp, Olga; Lounici, Karim; Tsybakov, Alexandre B.
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Universite Paris Saclay; University System of Georgia; Georgia Institute of Technology; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Humanities & Social Sciences (INSHS); Institut Polytechnique de Paris; ENSAE Paris
摘要：This paper considers the problem of estimation of a low-rank matrix when most of its entries are not observed and some of the observed entries are corrupted. The observations are noisy realizations of a sum of a low-rank matrix, which we wish to estimate, and a second matrix having a complementary sparse structure such as elementwise sparsity or columnwise sparsity. We analyze a class of estimators obtained as solutions of a constrained convex optimization problem combining the nuclear norm pe...
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作者：Fehrman, Benjamin J.
作者单位：Max Planck Society
摘要：The results of this paper build upon those first obtained by Sznitman and Zeitouni (Invent Math 164(3), 455-567, 2006). We establish, for spacial dimensions , the existence of a unique invariant measure for isotropic diffusions in random environment on which are small perturbations of Brownian motion. Furthermore, we establish a general homogenization result for initial data which are locally measurable with respect to the coefficients.
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作者：Belius, David; Kistler, Nicola
作者单位：New York University; Goethe University Frankfurt
摘要：The -cover time of the two dimensional torus by Brownian motion is the time it takes for the process to come within distance from any point. Its leading order in the small -regime has been established by Dembo et al. (Ann Math 160:433-464, 2004). In this work, the second order correction is identified. The approach relies on a multi-scale refinement of the second moment method, and draws on ideas from the study of the extremes of branching Brownian motion.
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作者：Izyurov, Konstantin
作者单位：University of Helsinki
摘要：We prove a general result on convergence of interfaces in the critical planar Ising model to conformally invariant curves absolutely continuous with respect to SLE(3). Our setup includes multiple interfaces on arbitrary finitely connected domains, and we also treat the radial SLE case. In the case of simply and doubly connected domains, the limiting processes are described explicitly in terms of rational and elliptic functions, respectively.
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作者：Miller, Jason; Wu, Hao
作者单位：University of Cambridge; University of Geneva
摘要：We compute the almost-sure Hausdorff dimension of the double points of chordal for , confirming a prediction of Duplantier-Saleur (1989) for the contours of the FK model. We also compute the dimension of the cut points of chordal for as well as analogous dimensions for the radial and whole-plane processes for . We derive these facts as consequences of a more general result in which we compute the dimension of the intersection of two flow lines of the formal vector field , where h is a Gaussian...
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作者：Sinclair, Alistair; Srivastava, Piyush; Stefankovic, Daniel; Yin, Yitong
作者单位：University of California System; University of California Berkeley; California Institute of Technology; University of Rochester; Nanjing University
摘要：We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model (which is defined as a weighted sum over all matchings where each matching is given a weight in terms of a fixed parameter called the monomer activity) and the hard core model (which is defined as a weighted sum over all independent sets where an independent...
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作者：Georgiou, Nicos; Rassoul-Agha, Firas; Seppalainen, Timo
作者单位：University of Sussex; Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. In Georgiou et al. (Probab Theory Relat Fields, 2016, doi:10.1007/s00440-016-0729-x) we constructed stationary cocycles and Busemann functions for this model. Using these objects, we prove new results on the competition interface, on existence, uniqueness, and coalescence of directional semi-infi...
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作者：Friz, Peter K.; Shekhar, Atul
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Technical University of Berlin
摘要：Existence of Loewner trace is revisited. We identify finite energy paths (the skeleton of Wiener measure) as natural class of regular drivers for which we find simple and natural estimates in terms of their (Cameron-Martin) norm. Secondly, now dealing with potentially rough drivers, a representation of the derivative of the (inverse of the) Loewner flow is given in terms of a rough- and then pathwise Follmer integral. Assuming the driver within a class of It-processes, an exponential martingal...
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作者：Croydon, David A.; Muirhead, Stephen
作者单位：University of Warwick; University of London; University College London; University of Oxford
摘要：We consider the quenched localisation of the Bouchaud trap model on the positive integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is that for each there exists a slowly varying tail such that quenched localisation occurs on exactly N sites. As far as we are aware, this is the first example of a model in which the exact number of localisation sites are able to be 'tuned' according to the model parameters. Key intuition for this result is pro...
