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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：Ding, Jian; Ma, Zongming; Wu, Yihong; Xu, Jiaming
作者单位：University of Pennsylvania; Yale University; Duke University
摘要：Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erdos-Renyi graphs G(n, d/n). This can be viewed as an average-case and noisy version of the graph isomorphism problem. Under this model, the maximum likelihood estimator is equivalent to solving the intractable quadratic assignment problem. This work develops an (O) over tilde (nd(2) + n(2))-time algorit...
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作者：Biskup, Marek; Chen, Xin; Kumagai, Takashi; Wang, Jian
作者单位：University of California System; University of California Los Angeles; Shanghai Jiao Tong University; Kyoto University; Fujian Normal University; Fujian Normal University; Fujian Normal University
摘要：We study random walks on Z(d) (with d >= 2) among stationary ergodic random conductances {C-x,C-y : x, y is an element of Z(d)} that permit jumps of arbitrary length. Our focus is on the quenched invariance principle (QIP) which we establish by a combination of corrector methods, functional inequalities and heat-kernel technology assuming that the p-th moment of Sigma(x is an element of Zd) C-0,C-x vertical bar x vertical bar(2) and q-th moment of 1/C-0,C-x for x neighboring the origin are fin...
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作者：Najnudel, Joseph; Virag, Balint
作者单位：University of Bristol; University of Toronto
摘要：The bead process introduced by Boutillier is a countable interlacing of the Sine(2) point processes. We construct the bead process for general Sine(beta) processes as an infinite dimensional Markov chain whose transition mechanism is explicitly described. We show that this process is the microscopic scaling limit in the bulk of the Hermite beta corner process introduced by Gorin and Shkolnikov, generalizing the process of the minors of the Gaussian Unitary and Orthogonal Ensembles. In order to...
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作者：Dimitrov, Evgeni; Wu, Xuan
作者单位：Columbia University; University of Chicago
摘要：In this paper we prove an analogue of the Komlos-Major-Tusnady (KMT) embedding theorem for random walk bridges. The random bridges we consider are constructed through random walks with i.i.d jumps that are conditioned on the locations of their endpoints. We prove that such bridges can be strongly coupled to Brownian bridges of appropriate variance when the jumps are either continuous or integer valued under some mild technical assumptions on the jump distributions. Our arguments follow a simil...
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作者：Yang, Fan; Yin, Jun
作者单位：University of Pennsylvania; University of California System; University of California Los Angeles
摘要：We consider a general class of symmetric or Hermitian random band matrices H = (h(xy))(x, y.)is an element of([1,N]d) in any dimension d >= 1, where the entries are independent, centered random variables with variances s(xy) = E-vertical bar hxy vertical bar 2. We assume that sxy vanishes if vertical bar x - y vertical bar exceeds the band width W, and we are interested in the mesoscopic scale with 1 << W << N. Define the generalized resolvent of H as G(H, Z) := (H - Z)(-1), where Z is a deter...
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作者：Chatterjee, Sourav; Diaconis, Persi
作者单位：Stanford University
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作者：Miller, Jason; Sheffield, Scott; Werner, Wendelin
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT); Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble CLE kappa' for kappa' in (4, 8) that is drawn on an independent gamma-LQG surface for gamma(2) = 16/kappa'. The results are similar in flavor to the ones from our companion paper dealing with CLE kappa for kappa in (8/3, 4), where the loops of the CLE are disjoint and simple. In particular, we encode the combined structure of the LQG surface and the CLE kappa' in te...
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作者：Caravenna, Francesco; den Hollander, Frank
作者单位：University of Milano-Bicocca; Leiden University - Excl LUMC; Leiden University
摘要：We consider a directed polymer of length N interacting with a linear interface. The monomers carry i.i.d. random charges (omega(i))(i=1)(N) taking values in R with mean zero and variance one. Each monomer i contributes an energy (beta omega(i) - h)phi(S-i) to the interaction Hamiltonian, where S-i is an element of Z is the height of monomer i with respect to the interface, phi : Z -> [0, infinity) is the interaction potential, beta is an element of [0, infinity) is the inverse temperature, and...
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作者：Cipolloni, Giorgio; Erdos, Laszlo; Schroeder, Dominik
作者单位：Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy-Widom distribution at the spectral edges of the Wigner ensemble.
