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作者：Hwang, Jong Yun; Lee, Ji Oon; Schnelli, Kevin
作者单位：Korea Advanced Institute of Science & Technology (KAIST); Royal Institute of Technology
摘要：We consider spectral properties of sparse sample covariance matrices, which includes biadjacency matrices of the bipartite Erdos-Renyi graph model. We prove a local law for the eigenvalue density up to the upper spectral edge. Under a suitable condition on the sparsity, we also prove that the limiting distribution of the rescaled, shifted extremal eigenvalues is given by the GOE Tracy-Widom law with an explicit formula on the deterministic shift of the spectral edge. For the biadjacency matrix...
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作者：Tameling, Carla; Sommerfeld, Max; Munk, Axel
作者单位：University of Gottingen
摘要：We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a delta method for nonlinear derivatives. A careful calibration of the norm on the space of probability measures is needed in order to combine differentiability and weak convergence of the underlying empirical process. Based on this, we provide a sufficient an...
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作者：Lachieze-Rey, Raphael
作者单位：Universite Paris Cite
摘要：This article presents a complete second-order theory for a large class of geometric functionals on homogeneous Poisson input. In particular, the results do not require the existence of a radius of stabilisation. Hence they can be applied to geometric functionals of spatial shot-noise fields excursions such as volume, perimeter, or Euler characteristic (the method still applies to stabilising functionals). More generally, it must be checked that a local contribution to the functional is not str...
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作者：Bayraktar, Erhan; Qiu, Jinniao
作者单位：University of Michigan System; University of Michigan; University of Calgary
摘要：We solve the optimal control problem of a one-dimensional reflected stochastic differential equation, whose coefficients can be path dependent. The value function of this problem is characterized by a backward stochastic partial differential equation (BSPDE) with Neumann boundary conditions. We prove the existence and uniqueness of a sufficiently regular solution for this BSPDE, which is then used to construct the optimal feedback control. In fact, we prove a more general result: the existence...
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作者：Monter, Sergio A. Almada; Shkolnikov, Mykhaylo; Zhang, Jiacheng
作者单位：JP Morgan Chase & Company; Princeton University; Princeton University; Princeton University
摘要：In the seminal work (Stochastic Portfolio Theory: Stochastic Modelling and Applied Probability (2002) Springer), several macroscopic market observables have been introduced, in an attempt to find characteristics capturing the diversity of a financial market. Despite the crucial importance of such observables for investment decisions, a concise mathematical description of their dynamics has been missing. We fill this gap in the setting of rank-based models. The results are then used to study th...
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作者：Bresler, Guy; Nagaraj, Dheeraj
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We develop a new technique, based on Stein's method, for comparing two stationary distributions of irreducible Markov chains whose update rules are close in a certain sense. We apply this technique to compare Ising models on d-regular expander graphs to the Curie-Weiss model (complete graph) in terms of pairwise correlations and more generally kth order moments. Concretely, we show that d-regular Ramanujan graphs approximate the kth order moments of the Curie-Weiss model to within average erro...
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作者：Jacob, Emmanuel; Linker, Amitai; Moerters, Peter
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile; University of Cologne
摘要：We study the contact process in the regime of small infection rates on finite scale-free networks with stationary dynamics based on simultaneous updating of all connections of a vertex. We allow the update rates of individual vertices to increase with the strength of a vertex, leading to a fast evolution of the network. We first develop an approach for inhomogeneous networks with general kernel and then focus on two canonical cases, the factor kernel and the preferential attachment kernel. For...
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作者：Marshall, Nicholas F.
作者单位：Yale University
摘要：Suppose f : [0, 1](2) -> R is a (c, alpha)-mixed Holder function that we sample at l points X-1,..., X-l chosen uniformly at random from the unit square. Let the location of these points and the function values f(X-1),..., f(X-l) be given. If l >= c(1)n log(2)n, then we can compute an approximation (f) over tilde such that parallel to integral -(integral) over tilde parallel to L-2 = O(n(-alpha) log(3/2)n), with probability at least 1- n(2-c1), where the implicit constant only depends on the c...
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作者：Gu, Yu; Tsai, Li-Cheng
作者单位：Carnegie Mellon University; Columbia University
摘要：For the heat equation driven by a smooth, Gaussian random potential: partial derivative(t)u(epsilon) = 1/2 Delta u epsilon + u(epsilon) (xi(epsilon) - c(epsilon)), t > 0, chi is an element of R, where xi(e) converges to a spacetime white noise, and c(epsilon) is a diverging constant chosen properly, we prove that u(epsilon) converges in L-n to the solution of the stochastic heat equation for any n >= 1. Our proof is probabilistic, hence provides another perspective of the general result of Hai...
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作者：Braunsteins, Peter; Hautphenne, Sophie
作者单位：University of Melbourne; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We consider a class of branching processes with countably many types which we refer to as Lower Hessenberg branching processes. These are multitype Galton-Watson processes with typeset X = {0, 1, 2,...}, in which individuals of type i may give birth to offspring of type j <= i + 1 only. For this class of processes, we study the set S of fixed points of the progeny generating function. In particular, we highlight the existence of a continuum of fixed points whose minimum is the global extinctio...
