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作者：Boutillier, Cedric; de Tiliere, Beatrice
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; University of Neuchatel
摘要：The dimer model on a graph embedded in the torus can be interpreted as a collection of random self-avoiding loops. In this paper, we consider the uniform toroidal honeycomb dimer model. We prove that when the mesh of the graph tends to zero and the aspect of the torus is fixed, the winding number of the collection of loops converges in law to a two-dimensional discrete Gaussian distribution. This is known to physicists in more generality from their analysis of toroidal two-dimensional critical...
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作者：Chen, Zhen-Qing; Zhang, Tusheng
作者单位：University of Washington; University of Washington Seattle; University of Manchester
摘要：In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have the maximum principle. Our method is probabilistic. The time reversal of symmetric Markov processes and the theory of Dirichlet forms play a crucial role in our approach.
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作者：Gine, Evarist; Nickl, Richard
作者单位：University of Connecticut; University of Cambridge
摘要：Let p(n)(y) = Sigma(k)(alpha) over cap (k)phi(y - k) + Sigma(jn-1)(l=0) Sigma(k)(beta) over cap (lk)2(l/2)psi(2(l) y-k) be the linear wavelet density estimator, where phi, psi are a father and a mother wavelet (with compact support), (alpha) over cap (k), (beta) over cap (lk) are the empirical wavelet coefficients based on an i.i.d. sample of random variables distributed according to a density p(0) on R, and j(n) is an element of Z, j(n) NE arrow infinity. Several uniform limit theorems are pr...
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作者：Evans, Steven N.
作者单位：University of California System; University of California Berkeley
摘要：We consider the asymptotic behavior as n -> infinity of the spectra of random matrices of the form 1/root n-1 (n-1)Sigma(k=1) Z(nk)rho(n) ((k, k + 1)), where for each n the random variables Z(nk) are i.i.d. standard Gaussian and the matrices rho(n) ((k, k + 1)) are obtained by applying an irreducible unitary representation rho(n) of the symmetric group on {1, 2,...,n} to the transposition (k, k + 1) that interchanges k and k + 1 [thus, rho(n) ((k, k + 1)) is both unitary and self-adjoint, with...
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作者：Dubins, Lester E.; Gilat, David; Meilijson, Isaac
作者单位：University of California System; University of California Berkeley; Tel Aviv University
摘要：It is shown that the ratio between the expected diameter of an L-2-bounded martingale and the standard deviation of its last term cannot exceed root 3. Moreover, I one-parameter family of stopping times on standard Brownian motion is exhibited, for which the root 3 upper bound is attained. These stopping times, one for each cost-rate c, are optimal when the payoff for stopping at time t is the diameter D(t) obtained up to time t minus the hitherto accumulated cost ct. A quantity related to dia...
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作者：Nourdin, Ivan; Peccati, Giovanni
作者单位：Sorbonne Universite; Universite Paris Cite; Universite Paris Nanterre; Universite Paris Saclay
摘要：We show how to detect optimal Berry-Esseen bounds in the normal approximation of functionals of Gaussian fields. Our techniques are based on a combination of Malliavin calculus, Stein's method and the method of moments and cumulants, and provide de facto local (one-term) Edgeworth expansions. The findings of the present paper represent a further refinement of the main results proven in Nourdin and Peccati [Probab. Theory Related Fields 145 (2009) 75-118]. Among several examples, we discuss thr...
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作者：Tudor, Ciprian A.; Viens, Frederi G.
作者单位：heSam Universite; Universite Pantheon-Sorbonne; Purdue University System; Purdue University; Purdue University System; Purdue University
摘要：Using multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic behavior of quadratic variations for a specific non-Gaussian self-similar process, the Rosenblatt process. We apply our results to the design of strongly consistent statistical estimators for the self-similarity parameter H. Although, in the case of the Rosenblatt process, our estimator has non-Gaussian asymptotics for all H > 1/2, we show the remarkable fact that the process's data at time 1 can be used ...
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作者：Taylor, Jonathan E.; Adler, Robert J.
作者单位：Stanford University; Technion Israel Institute of Technology
摘要：We consider vector valued, unit variance Gaussian processes defined over stratified manifolds and the geometry of their excursion sets. In particular, we develop an explicit formula for the expectation of all the Lipschitz-Killing curvatures of these sets. Whereas our motivation is primarily probabilistic, with statistical applications in the background, this formula has also an interpretation as a version of the classic kinematic fundamental formula of integral geometry. All of these aspects ...
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作者：Kurt, Noemi
作者单位：University of Zurich
摘要：We consider the real-valued centered Gaussian field on the four-dimensional integer lattice, whose covariance matrix is given by the Green's function of the discrete Bilaplacian. This is interpreted as a model for a semi-flexible membrane. d = 4 is the critical dimension for this model. We discuss the effect of a hard wall on the membrane, via a multiscale analysis of the maximum of the field. We use analytic and probabilistic tools to describe the correlation structure of the field.
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作者：Duquesne, Thomas
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：We prove that the total range of Super-Brownian motion with quadratic branching mechanism has an exact packing measure with respect to the gauge function g(r) = r(4)(log log l/r)(-3) in super-critical dimensions d >= 5. More precisely, we prove that the total occupation measure of Super-Brownian motion is equal to the g-packing measure restricted to its range, up to a deterministic multiplicative constant that only depends on space dimension d.
