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作者：El Alaoui, Ahmed; Montanari, Andrea
作者单位：Cornell University; Stanford University
摘要：We consider the problem of estimating a vector of discrete variables theta = (theta(1), ..., theta(n)), based on noisy observations Y-uv of the pairs (theta(u), theta(v)) on the edges of a graph G = ([n], E). This setting comprises a broad family of statistical estimation problems, including group synchronization on graphs, community detection, and low-rank matrix estimation. A large body of theoretical work has established sharp thresholds for weak and exact recovery, and sharp characterizati...
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作者：Gamarnik, David; Jagannath, Aukosh; Sen, Subhabrata
作者单位：Massachusetts Institute of Technology (MIT); University of Waterloo; University of Waterloo; Harvard University
摘要：We study support recovery for a k x k principal submatrix with elevated mean lambda/N, hidden in an N x N symmetric mean zero Gaussian matrix. Here lambda > 0 is a universal constant, and we assume k = N rho for some constant rho is an element of (0, 1). We establish that there exists a constant C > 0 such that the MLE recovers a constant proportion of the hidden submatrix if lambda >= C root 1/rho log 1/rho, while such recovery is information theoretically impossible if lambda = o(root 1/rho ...
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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：Ding, Jian; Gwynne, Ewain; Sepulveda, Avelio
作者单位：University of Pennsylvania; University of Chicago; Universidad de Chile
摘要：Discrete Liouville first passage percolation (LFPP) with parameter xi > 0 is the random metric on a sub-graph of Z(2) obtained by assigning each vertex z a weight of e(xi h(z)), where h is the discrete Gaussian free field. We show that the distance exponent for discrete LFPP is strictly positive for all xi > 0. More precisely, the discrete LFPP distance between the inner and outer boundaries of a discrete annulus of size 2(n) is typically at least 2(alpha n) for an exponent alpha > 0 depending...
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作者：Butkovsky, Oleg; Dareiotis, Konstantinos; Gerencser, Mate
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Leeds; Technische Universitat Wien
摘要：We give a new take on the error analysis of approximations of stochastic differential equations (SDEs), utilizing and developing the stochastic sewing lemma of Le (Electron J Probab 25:55, 2020. https://doi.org/10.1214/20-EJP442). This approach allows one to exploit regularization by noise effects in obtaining convergence rates. In our first application we show convergence (to our knowledge for the first time) of the Euler-Maruyama scheme for SDEs driven by fractional Brownian motions with non...
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作者：Marciniak, Mikolaj; Maslanka, Lukasz; Sniady, Piotr
作者单位：Nicolaus Copernicus University; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：We consider the Robinson-Schensted-Knuth algorithm applied to a random input and investigate the shape of the bumping route (in the vicinity of the y-axis) when a specified number is inserted into a large Plancherel-distributed random tableau. We show that after a projective change of the coordinate system the bumping route converges in distribution to the Poisson process.
