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作者：Michoel, T; Nachtergaele, B
作者单位：KU Leuven; University of California System; University of California Davis
摘要：We use a generalized form of Dyson's spin wave formalism to prove several central limit theorems for the large-spin asymptotics of quantum spins in a coherent state.
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作者：Forrester, PJ; Rains, EM
作者单位：University of Melbourne; AT&T
摘要：A superposition of a matrix ensemble refers to the ensemble constructed from two independent copies of the original, while a decimation refers to the formation of a new ensemble by observing only every second eigenvalue. In the cases of the classical matrix ensembles with orthogonal symmetry, it is known that forming superpositions and decimations gives rise to classical matrix ensembles with unitary and symplectic symmetry. The basic identities expressing these facts can be extended to includ...
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作者：Lawler, GF; Werner, W
作者单位：Cornell University; Universite Paris Saclay
摘要：We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to chronologically add Brownian loops to simple curves in the plane.
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作者：Kim, KH
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Stochastic partial differential equations of divergence form are considered in C-1 domains. Existence and uniqueness results are given in a Sobolev space with weights allowing the derivatives of the solutions to blow up near the boundary.
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作者：Wu, TJ; Tsai, MH
作者单位：National Cheng Kung University
摘要：Based on a random sample of size n from an unknown d-dimensional density f, the problem of selecting the bandwidths in kernel estimation of f is investigated. The optimal root n relative convergence rate for bandwidth selection is established and the information bounds in this convergence are given, and a stabilized bandwidth selector (SBS) is proposed. It is known that for all d the bandwidths selected by the least squares cross-validation (LSCV) have large sample variations. The proposed SBS...
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作者：Abraham, R; Delmas, JF
作者单位：Universite Paris Cite; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：We consider a Brownian snake (W-s, s greater than or equal to 0) with underlying process a reflected Brownian motion in a bounded domain D. We construct a continuous additive functional (L-s, s greater than or equal to0) of the Brownian snake which counts the time spent by the end points (W) over cap (s) of the Brownian snake paths on partial derivativeD. The random measure Z = integraldelta(delta) over cap (s) dL(s) is supported by partial derivativeD. Then we represent the solution v of Delt...
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作者：Chen, ZQ; Kim, P
作者单位：University of Washington; University of Washington Seattle
摘要：Recently the authors showed that the Martin boundary and the minimal Martin boundary for a censored (or resurrected) alpha-stable process Y in a bounded C-1,C-1-open set D with alpha is an element of (1, 2 can all be identified with the Euclidean boundary D of D. Under the gaugeability assumption, we show that the Martin boundary and the minimal Martin boundary for the Schrodinger operator obtained from Y through a non-local Feynman-Kac transform can all be identified with partial derivativeD....
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作者：Eichelsbacher, P; Löwe, M
作者单位：Ruhr University Bochum; University of Munster
摘要：We derive moderate deviation principles for the overlap parameter in the Hopfield model of spin glasses and neural networks. If the inverse temperature beta is different from the critical inverse temperature beta(c)=1 and the number of patterns M(N) satisfies M(N)/N --> 0, the overlap parameter multiplied by N-gamma, 1/2 < gamma < 1, obeys a moderate deviation principle with speed N1-2gamma and a quadratic rate function (i.e. the Gaussian limit for gamma = 1/2 remains visible on the moderate d...
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作者：Nazarov, AL; Nikitin, YY
作者单位：Saint Petersburg State University
摘要：We find the exact small deviation asymptotics for the L-2-norm of various m- times integrated Gaussian processes closely connected with the Wiener process and the Ornstein - Uhlenbeck process. Using a general approach from the spectral theory of linear differential operators we obtain the two-term spectral asymptotics of eigenvalues in corresponding boundary value problems. This enables us to improve the recent results from [15] on the small ball asymptotics for a class of m-times integrated W...
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作者：Yoshida, N
作者单位：University of Tokyo
摘要：Introducing a conditional mixing property, Gotze and Hipp's theory is generalized to a continuous-time conditional epsilon-Markov process satisfying this property. The Malliavin calculus for jump processes applies to random-coefficient stochastic differential equations with jumps with the aid of the support theorem to verify the non-degeneracy condition, i.e., a conditional type Cramer condition.
