Probability Theory and Related Fields

最新文章

• Exit problems associated with affine reflection groups AI翻译
  作者：Doumerc, Yan; Moriarty, John
  作者单位：University of Manchester
  摘要：We obtain a formula for the distribution of the first exit time of Brownian motion from the alcove of an affine Weyl group. In most cases the formula is expressed compactly, in terms of Pfaffians. Expected exit times are derived in the type (A) over tilde case. The results extend to other Markov processes. We also give formulas for the real eigenfunctions of the Dirichlet and Neumann Laplacians on alcoves, observing that the 'Hot Spots' conjecture of J. Rauch is true for alcoves.
• Aggregation via empirical risk minimization AI翻译
  作者：Lecue, Guillaume; Mendelson, Shahar
  作者单位：Australian National University; Technion Israel Institute of Technology
  摘要：Given a finite set F of estimators, the problem of aggregation is to construct a new estimator whose risk is as close as possible to the risk of the best estimator in F. It was conjectured that empirical minimization performed in the convex hull of F is an optimal aggregation method, but we show that this conjecture is false. Despite that, we prove that empirical minimization in the convex hull of a well chosen, empirically determined subset of F is an optimal aggregation method.
• Sharp probability estimates for random walks with barriers AI翻译
  作者：Ford, Kevin
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign
  摘要：We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y, infinity) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided the fourth moment is finite.
• The exact packing measure of Brownian double points AI翻译
  作者：Morters, Peter; Shieh, Narn-Rueih
  作者单位：University of Bath; National Taiwan University
  摘要：Let D subset of R-3 be the set of double points of a three-dimensional Brownian motion. We show that, if xi = xi 3(2, 2) is the intersection exponent of two packets of two independent Brownian motions, then almost surely, the phi-packing measure of D is zero if integral(0+) r(-1-xi)phi(r)(xi) dr < infinity, and infinity otherwise. As an important step in the proof we show up-to-constants estimates for the tail at zero of Brownian intersection local times in dimensions two and three.
• Kinetically constrained spin models AI翻译
  作者：Cancrini, N.; Martinelli, F.; Roberto, C.; Toninelli, C.
  作者单位：Roma Tre University; University of L'Aquila; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：We analyze the density and size dependence of the relaxation time for kinetically constrained spin models (KCSM) intensively studied in the physics literature as simple models sharing some of the features of the glass transition. KCSM are interacting particle systems on Z(d) with Glauber-like dynamics, reversible w.r.t. a simple product i.i.d Bernoulli(p) measure. The essential feature of a KCSM is that the creation/destruction of a particle at a given site can occur only if the current config...
• Large deviations for sums indexed by the generations of a Galton-Watson process AI翻译
  作者：Fleischmann, Klaus; Wachtel, Vitali
  作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Munich
  摘要：In this paper, we study the large deviation behavior of sums SZ(n) of i.i.d. random variables X-i, where Z(n) is the nth generation of a supercritical Galton Watson process. We assume the finiteness of the moments EX12 and EZ(1)logZ(1). The underlying interplay of large deviation probabilities of partial sums of the X-i and of lower deviation probabilities of Z is clarified. Here, we heavily use lower deviation probability results on Z we recently published in [7].
• Uniform central limit theorems for Kernel density estimators AI翻译
  作者：Gine, Evarist; Nickl, Richard
  作者单位：University of Connecticut
  摘要：Let Pn* K-hn (x) = n(-1)h(n)(-d) Sigma(n)(i= 1) K (( x - X-i)/h(n)) be the classical kernel density estimator based on a kernel K and n independent random vectors X-i each distributed according to an absolutely continuous law P on R-d. It is shown that the processes f ->root n f d(P-n * K-hn - P), f is an element of F, converge in law in the Banach space l infinity(F), for many interesting classes F of functions or sets, some P- Donsker, some just P- pregaussian. The conditions allow for the c...
• Threshold θ ≥ 2 contact processes on homogeneous trees AI翻译
  作者：Fontes, Luiz Renato; Schonmann, Roberto H.
  作者单位：University of California System; University of California Los Angeles
  摘要：We study the threshold theta >= 2 contact process on a homogeneous tree T-b of degree k = b + 1, with infection parameter lambda >= 0 and started from a product measure with density p. The corresponding mean-field model displays a discontinuous transition at a critical point lambda(MF)(c) (k, theta) and for lambda >= lambda(MF)(c) (k, theta) it survives iff p >= p(c)(MF)(k, theta, lambda), where this critical density satisfies 0 < p(c)(MF)(k,theta,lambda) < 1, lim(lambda ->infinity) p(cMF)(k,t...
• Perturbation of symmetric Markov processes AI翻译
  作者：Chen, Z.-Q.; Fitzsimmons, P. J.; Kuwae, K.; Zhang, T.-S.
  作者单位：University of California System; University of California San Diego; University of Washington; University of Washington Seattle; Kumamoto University; University of Manchester
  摘要：We present a path-space integral representation of the semigroup associated with the quadratic form obtained by a lower-order perturbation of the L-2-infinitesimal generator L of a general symmetric Markov process. An illuminating concrete example for L is Delta(D)- (-Delta)(s)(D), where D is a bounded Euclidean domain in R-d, s epsilon [ 0, 1], Delta(D) is the Laplace operator in D with zero Dirichlet boundary condition and -(-Delta)(D)(s) is the fractional Laplacian in D with zero exterior c...
• Some results for long-range exclusion processes AI翻译
  作者：Andjel, Enrique; Mountford, T. S.
  作者单位：Aix-Marseille Universite; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
  摘要：We examine the long-range exclusion process introduced by Spitzer and studied by Liggett and answer some of the open questions raised by Liggett. In particular, we show the existence of equilibria corresponding to bounded dual harmonic functions and that the process can have right-discontinuous paths at strictly positive times. We also show that explosions when they occur, do so at fixed times determined by the initial configuration. Finally, we give an example for which the configuration with...