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作者：Doeringa, Leif; Trottnerb, Lukas
作者单位：University of Mannheim
摘要：We prove precise stability results for overshoots of Markov additive processes (MAPs) with finite modulating space. Our approach is based on the Markovian nature of overshoots of MAPs whose mixing and ergodic proper-ties are investigated in terms of the characteristics of the MAP. On our way we extend fluctuation theory of MAPs, contributing among others to the understanding of the Wiener-Hopf factorization for MAPs by generalizing Vigon's equations amicales inverses known for Levy processes. ...
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作者：Gamarnik, David; Kizildag, Eren c.
作者单位：Massachusetts Institute of Technology (MIT); Columbia University
摘要：We consider the algorithmic problem of finding a near-optimal solution for the number partitioning problem (NPPNPP). This problem appears in many practical applications, including the design of randomized controlled trials, multiprocessor scheduling, and cryptography. It is also of theoretical significance. The NPPNPP possesses a so-called statistical-to-computational gap: when its input X has distribution N(0,In), the optimal value of the NPPNPP is Theta(root n2(-n))w.h.p., whereas the best-k...
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作者：Li, Yiting
作者单位：Korea Advanced Institute of Science & Technology (KAIST)
摘要：For a beta ensemble on Sigma((N)) = {(x(1),... , x(N)) is an element of R-N |x(1) <= center dot center dot center dot <= x(N)} with real analytic potential and general beta > 0, under the assumption that its equilibrium measure is supported on q intervals where q > 1, we prove the following rigidity property for its particles. 1. In the bulk of the spectrum, with overwhelming probability, the distance between a particle and its classical position is of order O (N-1+epsilon). 2. If k is close t...
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作者：Bansaye, Vincent; Gu, Chenlin; Yuan, Linglong
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Tsinghua University; University of Liverpool
摘要：We consider a random process on recursive trees, with three types of events. Vertices give birth at a constant rate (growth), each edge may be re-moved independently (fragmentation of the tree) and clusters (or trees) are frozen with a rate proportional to their sizes (isolation of connected compo-nent). A phase transition occurs when the isolation is able to stop the growth -fragmentation process and cause extinction. When the process survives, the number of clusters increases exponentially a...
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作者：Bouchard, Bruno; Loeper, Gregoire; Tan, Xiaolu
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Monash University; Monash University; Chinese University of Hong Kong
摘要：We introduce a notion of approximate viscosity solutions for a class of nonlinear path-dependent PDEs (PPDEs), including the Hamilton-Jacobi- Bellman-type equations. Existence, comparaison and stability results have been established under fairly general conditions. It is also consistent with the notion of smooth solution when the dimension is less or equal to two, or the nonlinearity is concave in the second order space derivative. We finally investigate the regularity (in the sense of Dupire)...
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作者：Da Costa, Conrado; Menshikov, Mikhail, V; Wade, Andrew r.
作者单位：Durham University
摘要：We study recurrence and transience for a particle that moves at constant velocity in the interior of an unbounded planar domain, with random reflections at the boundary governed by a Markov kernel producing outgoing angles from incoming angles. Our domains have a single unbounded direction and sub-linear growth. We characterize recurrence in terms of the reflection kernel and growth rate of the domain. The results are obtained by transform-ing the stochastic billiards model to a Markov chain o...
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作者：He, Jimmy; Ottolini, Andrea
作者单位：Massachusetts Institute of Technology (MIT); University of Washington; University of Washington Seattle
摘要：Consider a uniformly random deck consisting of cards labelled by num-bers from 1 through n , possibly with repeats. A guesser guesses the top card, after which it is revealed and removed and the game continues. What is the expected number of correct guesses under the best and worst strategies? We establish sharp asymptotics for both strategies. For the worst case, this an-swers a recent question of Diaconis, Graham, He and Spiro, who found the correct order. As part of the proof, we study the ...
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作者：Bao, Zhigang; He, Yukun
作者单位：Hong Kong University of Science & Technology; City University of Hong Kong
摘要：In this article, we establish a near-optimal convergence rate for the CLT of linear eigenvalue statistics of N x N Wigner matrices, in Kolmogorov- Smirnov distance. For all test functions f is an element of C5(R), we show that the conver-gence rate is either N-1/2+epsilon or N-1+epsilon, depending on the first Chebyshev coefficient of f and the third moment of the diagonal matrix entries. The condition that distinguishes these two rates is necessary and sufficient. For a general class of test ...
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作者：Coghi, Michele; Nilssen, Torstein; Nuesken, Nikolas; Reich, Sebastian
作者单位：University of Trento; University of Agder; University of London; King's College London; University of Potsdam
摘要：Motivated by the challenge of incorporating data into misspecified and multiscale dynamical models, we study a McKean-Vlasov equation that contains the data stream as a common driving rough path. This setting allows us to prove well-posedness as well as continuity with respect to the driver in an appropriate rough-path topology. The latter property is key in our subsequent development of a robust data assimilation methodology: We establish propagation of chaos for the associated interacting pa...
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作者：Ben Arous, Gerard; Huang, Daniel Zhengyu; Huang, Jiaoyang
作者单位：New York University; Peking University; University of Pennsylvania
摘要：In this paper, we consider the singular values and singular vectors of low rank perturbations of large rectangular random matrices, in the regime the matrix is long: we allow the number of rows (columns) to grow polynomi-ally in the number of columns (rows). We prove there exists a critical signal-to-noise ratio (depending on the dimensions of the matrix), and the extreme singular values and singular vectors exhibit a BBP-type phase transition. As a main application, we investigate the tensor ...
