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21.
Michel Talagrand 《Israel Journal of Mathematics》1984,47(1):75-80
We construct a Banach space which is weak*-countably determined in its second dual, but which is notK-analytic for its weak topology.
This paper was written while the author was visiting The Ohio State University. 相似文献
22.
Michel Talagrand 《Comptes Rendus Mathematique》2003,337(9):625-628
The author has recently proved that a famous formula discovered by G. Parisi gives at any temperature the correct value for the limiting free energy of a large class of mean field models for spin glasses (a class which contains in particular the Sherrington–Kirkpatrick model). Here we prove rigorously that (generically) the “functional order parameter” occuring in this formula can be interpreted as predicted by Parisi, namely as representing the limiting distribution of the overlap of two independent configurations. To cite this article: M. Talagrand, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
23.
24.
We show that a Banach space valued random variableX such that
t} \right\} = 0$$
" align="middle" border="0">
satisfies the central limit theorem if and only if the following criterion on small balls is fulfilled:
t} \right\} = 0$$
" align="middle" vspace="20%" border="0"> 相似文献
25.
Donsker classes of sets 总被引:1,自引:0,他引:1
Michel Talagrand 《Probability Theory and Related Fields》1988,78(2):169-191
Summary We study the central limit theorem (CLT) and the law of large numbers (LLN) for empirical processes indexed by a (countable) class of sets C. The main result, of purely measure-theoretical nature, relates different ways to measure the size of C. It relies on a new rearrangement inequality that has been inspired by techniques used in the local theory of Banach spaces. As an application, we give sharp necessary conditions for the CLT, that are in some sense the best possible. We also obtain a way to compute the rate of convergence in the LLN. 相似文献
26.
LetX(t) (tR
N
) be a fractional Brownian motion of index inR
d
. For any compact setER
N
, we compute the packing dimension ofX(E).Partially supported by an NSF grant. 相似文献
27.
Given a collection of items and a number of unit size bins, the dual bin packing problem requires finding the largest number of items that can be packed in these bins. In our stochastic model, the item sizesX
1,,X
n
are independent identically distributed according to a given probability measure. Denote byN
n
=N
n
(X
1,,X
n
) the largest number of these items that can be packed in an bins, where 0<a<1 is a constant. We show thatb = lim
n
E(N
n
)/n exists, and that the random variable (N
n
–nb)/
converges in distribution. The limit is identified as the distribution of the supremum of a certain Gaussian process cannonically attached to.
This research is in part supported by NSF grant CCR-8801517 and CCR-9000611.This research is in part supported by NSF grant DMS-8801180. 相似文献
28.
Michel Talagrand 《Probability Theory and Related Fields》2009,143(1-2):97-111
Given numbers a ij ≥ 0 for 1 ≤ i < j ≤ N, and given numbers b i ≥ 0, i ≤ N, we consider the random Hamiltonian $\sum_{i,j \le N} \sqrt{a_{ij}} g_{ij} \sigma_i \sigma_j + \sum_{i \le N} \sqrt{b_i} g_i \sigma_i$ , where g i , g ij denote independent standard normal r.v., and where σ i = ± 1. We give sufficient conditions on the coefficients a ij for the system governed by this Hamiltonian to exhibit “high-temperature behavior”. There results extend known facts concerning the behavior of the Sherrington-Kirkpatrick model at “very high-temperature”. In a similar manner we give a general form of the “perceptron model”. 相似文献
29.
Michel Talagrand 《Probability Theory and Related Fields》2006,135(4):471-486
Consider the random subset X of ℕ obtained by selecting independently each integer with a probability δ. Consider a finite class of finite sets. We describe a combinatorial quantity that is of the same order as We then give a related result allowing to compute the supremum of the empirical process on a class of sets.
Work partially supported by an NSF grant. 相似文献
30.
Michel Talagrand 《Random Structures and Algorithms》1999,14(3):199-213
We prove (through a precise exponential inequality) that the logarithm of the size of the intersection of M random half spaces with the unit sphere of ℝN (resp., the discrete cube {−1, 1}N) is, as N→∞, a self averaging quantity. This provides justification for one of the first steps of a famous computation by E. Gardner [J. Phys. A 21 (1988), 257–270]. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 199–213, 1999 相似文献
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