共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
3.
Guan-Yu Chen 《Journal of Functional Analysis》2003,202(2):473-485
Consider the simple random walk on the n-cycle . For this example, Diaconis and Saloff-Coste (Ann. Appl. Probab. 6 (1996) 695) have shown that the log-Sobolev constant α is of the same order as the spectral gap λ. However the exact value of α is not known for n>4. (For n=2, it is a well known result of Gross (Amer. J. Math. 97 (1975) 1061) that α is . For n=3, Diaconis and Saloff-Coste (Ann. Appl. Probab. 6 (1996) 695) showed that . For n=4, the fact that follows from n=2 by tensorization.) Based on an idea that goes back to Rothaus (J. Funct. Anal. 39 (1980) 42; 42 (1981) 110), we prove that if n?4 is even, then the log-Sobolev constant and the spectral gap satisfy . This implies that when n is even and n?4. 相似文献
4.
5.
Enkelejd Hashorva 《Journal of multivariate analysis》2010,101(4):926-935
In this paper we consider elliptical random vectors in Rd,d≥2 with stochastic representation , where R is a positive random radius independent of the random vector which is uniformly distributed on the unit sphere of Rd and A∈Rd×d is a given matrix. Denote by ‖⋅‖ the Euclidean norm in Rd, and let F be the distribution function of R. The main result of this paper is an asymptotic expansion of the probability for F in the Gumbel or the Weibull max-domain of attraction. In the special case that is a mean zero Gaussian random vector our result coincides with the one derived in Hüsler et al. (2002) [1]. 相似文献
6.
7.
8.
Amine Asselah Fabienne Castell 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2007,43(2):163
We consider a random walk in random scenery {Xn=η(S0)+?+η(Sn),n∈N}, where a centered walk {Sn,n∈N} is independent of the scenery {η(x),x∈Zd}, consisting of symmetric i.i.d. with tail distribution P(η(x)>t)∼exp(−cαtα), with 1?α<d/2. We study the probability, when averaged over both randomness, that {Xn>ny} for y>0, and n large. In this note, we show that the large deviation estimate is of order exp(−ca(ny)), with a=α/(α+1). 相似文献
9.
Fatma Ghribi 《Journal of Functional Analysis》2007,248(2):387-427
This paper is devoted to the study of Lifshits tails for weak random magnetic perturbations of periodic Schrödinger operators acting on L2(Rd) of the form Hλ,w=(−i∇−λ∑γ∈ZdwγA2(⋅−γ))+V, where V is a Zd-periodic potential, λ is positive coupling constants, (wγ)γ∈Zd are i.i.d and bounded random variables and is the single site vector magnetic potential. We prove that, for λ small, at an open band edge, a true Lifshits tail for the random magnetic Schrödinger operator occurs if a certain set of conditions on H0=−Δ+V and on A holds. 相似文献
10.
11.
12.
Moritz Jirak 《Journal of multivariate analysis》2011,102(6):1032-1046
13.
Mark M. Meerschaert Erkan Nane Yimin Xiao 《Journal of Mathematical Analysis and Applications》2008,346(2):432-445
Let be a fractional Brownian motion of Hurst index H∈(0,1) with values in R, and let be the local time process at zero of a strictly stable Lévy process of index 1<α?2 independent of WH. The α-stable local time fractional Brownian motion is defined by ZH(t)=WH(Lt). The process ZH is self-similar with self-similarity index and is related to the scaling limit of a continuous time random walk with heavy-tailed waiting times between jumps [P. Becker-Kern, M.M. Meerschaert, H.P. Scheffler, Limit theorems for coupled continuous time random walks, Ann. Probab. 32 (2004) 730-756; M.M. Meerschaert, H.P. Scheffler, Limit theorems for continuous time random walks with infinite mean waiting times, J. Appl. Probab. 41 (2004) 623-638]. However, ZH does not have stationary increments and is non-Gaussian. In this paper we establish large deviation results for the process ZH. As applications we derive upper bounds for the uniform modulus of continuity and the laws of the iterated logarithm for ZH. 相似文献
14.
15.
16.
Daniel Simson 《Journal of Pure and Applied Algebra》2011,215(1):13-34
Integral quadratic forms q:Zn→Z, with n≥1, and the sets Rq(d)={v∈Zn;q(v)=d}, with d∈Z, of their integral roots are studied by means of mesh translation quivers defined by Z-bilinear morsifications bA:Zn×Zn→Z of q, with Z-regular matrices A∈Mn(Z). Mesh geometries of roots of positive definite quadratic forms q:Zn→Z are studied in connection with root mesh quivers of forms associated to Dynkin diagrams An,Dn,E6,E7,E8 and the Auslander-Reiten quivers of the derived category Db(R) of path algebras R=KQ of Dynkin quivers Q. We introduce the concepts of a Z-morsification bA of a quadratic form q, a weighted ΦA-mesh of vectors in Zn, and a weighted ΦA-mesh orbit translation quiver Γ(Rq,ΦA) of vectors in Zn, where Rq?Rq(1) and ΦA:Zn→Zn is the Coxeter isomorphism defined by A. The existence of mesh geometries on Rq is discussed. It is shown that, under some assumptions on the morsification bA:Zn×Zn→Z, the set admit a ΦA-orbit mesh quiver , where ΦA:Zn→Zn is the Coxeter isomorphism defined by A. Moreover, splits into three infinite connected components , , and , where are isomorphic to a translation quiver Z⋅Δ, with Δ an extended Dynkin quiver, and has the shape of a sand-glass tube. 相似文献
17.
We consider the periodic Zakharov-Shabat operators on the real line. The spectrum of this operator consists of intervals separated by gaps with the lengths |gn|?0, n∈Z. Let be the corresponding effective masses and let hn be heights of the corresponding slits in the quasi-momentum domain. We obtain a priori estimates of sequences g=(|gn|)n∈Z, , h=(hn)n∈Z in terms of weighted ?p-norms at p?1. The proof is based on the analysis of the quasi-momentum as the conformal mapping. 相似文献
18.
19.
Songqiao Wen 《Journal of multivariate analysis》2007,98(4):743-756
Let X1,X2,…,Xn be independent exponential random variables such that Xi has failure rate λ for i=1,…,p and Xj has failure rate λ* for j=p+1,…,n, where p≥1 and q=n-p≥1. Denote by Di:n(p,q)=Xi:n-Xi-1:n the ith spacing of the order statistics , where X0:n≡0. It is shown that Di:n(p,q)?lrDi+1:n(p,q) for i=1,…,n-1, and that if λ?λ* then , and for i=1,…,n, where ?lr denotes the likelihood ratio order. The main results are used to establish the dispersive orderings between spacings. 相似文献