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作者：Holroyd, Alexander E.; Marcovici, Irene; Martin, James B.
作者单位：Universite de Lorraine; University of Oxford
摘要：Let each site of the square lattice Z2 be independently assigned one of three states: a trap with probability p, a target with probability q, and open with probability 1-p-q, where 0<1. Consider the following game: a token starts at the origin, and two players take turns to move, where a move consists of moving the token from its current site x to either x+(0,1) or x+(1,0). A player who moves the token to a trap loses the game immediately, while a player who moves the token to a target wins th...
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作者：Brunel, Victor-Emmanuel
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Tukey's halfspace depth has attracted much interest in data analysis, because it is a natural way of measuring the notion of depth relative to a cloud of points or, more generally, to a probability measure. Given an i.i.d. sample, we investigate the concentration of upper level sets of the Tukey depth relative to that sample around their population version. We show that under some mild assumptions on the underlying probability measure, concentration occurs at a parametric rate and we deduce mo...
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作者：Filmus, Yuval; Mossel, Elchanan
作者单位：Technion Israel Institute of Technology; Massachusetts Institute of Technology (MIT)
摘要：In a recent work with Kindler and Wimmer we proved an invariance principle for the slice for low-influence, low-degree harmonicmultilinear polynomials (a polynomial in x1,..., xn is harmonic if it is annihilated by n i=1.. xi). Here we provide an alternative proof for general low-degree harmonicmultilinear polynomials, with no constraints on the influences. We show that any real-valued harmonic multilinear polynomial on the slice whose degree is o(v n) has approximately the same distribution u...
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作者：Heydenreich, Markus; van der Hofstad, Remco
作者单位：Vrije Universiteit Amsterdam; Eindhoven University of Technology
摘要：In [3, Theorem 1.2], we claim that the maximal cluster for critical percolation on the high-dimensional torus is non-concentrated. This proof contains an error. In this note, we replace this statement by a conditional statement instead.
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作者：Forrester, Peter J.; Ipsen, Jesper R.
作者单位：University of Melbourne
摘要：The zeros of the random Laurent series 1/mu - 8 j=1 c j / z j, where each c j is an independent standard complex Gaussian, is known to correspond to the scaled eigenvalues of a particular additive rank 1 perturbation of a standard complex Gaussian matrix. For the corresponding random Maclaurin series obtained by the replacement z . 1/ z, we show that these same zeros correspond to the scaled eigenvalues of a particular multiplicative rank 1 perturbation of a random unitary matrix. Since the co...
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作者：Berestycki, Nathanael; Sengul, Bati
作者单位：University of Cambridge
摘要：We prove a conjecture raised by the work of Diaconis and Shahshahani (Z Wahrscheinlichkeitstheorie Verwandte Geb 57(2):159-179, 1981) about the mixing time of random walks on the permutation group induced by a given conjugacy class. To do this we exploit a connection with coalescence and fragmentation processes and control the Kantorovich distance by using a variant of a coupling due to Oded Schramm as well as contractivity of the distance. Recasting our proof in the language of Ricci curvatur...
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作者：Powell, Ellen
摘要：We study branching diffusions in a bounded domain D of Rd in which particles are killed upon hitting the boundary D. It is known that any such process undergoes a phase transition when the branching rate exceeds a critical value: a multiple of the first eigenvalue of the generator of the diffusion. We investigate the system at criticality and show that the associated genealogical tree, when the process is conditioned to survive for a long time, converges to Aldous' Continuum Random Tree under ...
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作者：Bally, Vlad; Caramellino, Lucia; Poly, Guillaume
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); University of Rome Tor Vergata; Universite de Rennes
摘要：In this article, we consider the following family of random trigonometric polynomials pn(t,Y)=Sigma k=1nYk1cos(kt)+Yk2sin(kt) for a given sequence of i.i.d. random variables Yki, i is an element of{1,2}, k >= 1, which are centered and standardized. We set N([0,pi],Y) the number of real roots over [0,pi] and N([0,pi],G) the corresponding quantity when the coefficients follow a standard Gaussian distribution. We prove under a Doeblin's condition on the distribution of the coefficients that lim (...
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作者：Naumov, Alexey; Spokoiny, Vladimir; Ulyanov, Vladimir
作者单位：HSE University (National Research University Higher School of Economics); Russian Academy of Sciences; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Lomonosov Moscow State University
摘要：Let X1, ... ,X-n be i.i.d. sample in Rp with zero mean and the covariance matrix Sigma. The problem of recovering the projector onto an eigenspace of Sigma from these observations naturally arises in many applications. Recent technique from Koltchinskii and Lounici (Ann Stat 45(1):121-157,2017) helps to study the asymptotic distribution of the distance in the Frobenius norm parallel to P-r-(P) over cap (r)parallel to(2) between the true projector Pr on the subspace of the rth eigenvalue and it...
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作者：Kabluchko, Zakhar; Marynych, Alexander; Temesvari, Daniel; Thaele, Christoph
作者单位：University of Munster; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; Ruhr University Bochum
摘要：Let U1, U2,... be random points sampled uniformly and independently from the d-dimensional upper half-sphere. We showthat, as n.8, the f -vector of the (d+1)-dimensional convex cone Cn generated by U1,..., Un weakly converges to a certain limiting random vector, without any normalization. We also show convergence of all moments of the f -vector of Cn and identify the limiting constants for the expectations. We prove that the expected Grassmann angles of Cn can be expressed through the expected...
