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1.
Michel Talagrand 《Israel Journal of Mathematics》1989,68(1):82-88
There exists a non-Dunford-Pettis operator fromL
1 into a Banach latticeE that does not contain a copy ofc
0 orL
1. This problem is related to regularisation properties of convolution operators onL
1.
Work partially supported by an N.S.F. Grant. 相似文献
2.
Michel Talagrand 《Comptes Rendus Mathematique》2003,337(7):477-480
Consider a random Hamiltonian for We assume that the family is jointly Gaussian centered and that for =ξ(N?1∑i?Nσ1iσ2i) for a certain function ξ on . F. Guerra proved the remarkable fact that the free energy of the system with Hamiltonian is bounded below by the free energy of the Parisi solution provided that ξ is convex on . We prove that this fact remains (asymptotically) true when the function ξ is only assumed to be convex on . This covers in particular the case of the p-spin interaction model for any p. To cite this article: M. Talagrand, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
3.
M. Talagrand 《Geometric And Functional Analysis》1993,3(3):295-314
We prove that the suitably defined surface area of a subsetA of the cube {0,1}
n
is bounded below by a certain explicit function of the size ofA. We establish a family of logarithmic Sobolev inequalities on the cube related to this isoperimetric result. We also give a quantitative version of Margulis' graph connectivity theorem.Work partially supported by the US-Israel Binational Science Foundation. 相似文献
4.
Michel Talagrand 《Probability Theory and Related Fields》2006,134(3):339-382
We compute at any temperature the free energy of the multi p-spin spherical model when only terms for p even are considered.
Work partially supported by an NSF grant 相似文献
5.
Michel Talagrand 《Inventiones Mathematicae》1992,107(1):1-40
Summary Forq>2, an operator fromC(K) toX is of cotypeq if and only if it factors through the Lorentz space
. Forq=2, ifX is a rearrangement invariant space on [0, 1], the injectionC([0, 1])X is of cotype 2 if and only if it factors through the Lorentz space
; but there is a cotype 2 operator C(K) that does not factor through
. If a Banach latticeX satisfies the Orlicz property, any bounded lattice operatorT:C(K)X is of cotype 2. We however construct a Banach lattice with the Orlicz property, but that fails to be of cotype 2.Oblatum 4-VII-1990 & 18-IV-1991Work partially supported by an NSF grant 相似文献
6.
Michel Talagrand 《Journal of Theoretical Probability》1992,5(2):327-331
Consider a (complex) Banach spaceX, such thatX CO, and vectors(X
i
)
i
ofX. Consider an independent standard normal sequence(g
i
)
i
. Then if anX-valued random Fourier series |k|
n
e
ikt
g
k
x
k
satisfies
相似文献
7.
Michel Talagrand 《Probability Theory and Related Fields》1981,57(2):213-221
Summary We give a simple proof of the fact that a Radon gaussian measure on a locally convex vector space is carried by a countable union of metrisable compact sets. We show that a separable centered gaussian process with continuous covariance which is defined on a Polish space X, and is a.e. unbounded on any open set, has a.e. dense trajectories in X × . These results allow us to show that for any set I, any gaussian measure on
I
is -smooth. 相似文献
8.
Michel Talagrand 《Mathematische Annalen》1979,240(2):97-102
Resumé On construit un groupe compact et une sous-mesure pathologique sur ce groupe dont la convolée avec la mesure de Haar n'est pas pathologique. 相似文献
9.
Michel Talagrand 《Probability Theory and Related Fields》1998,112(4):545-563
Consider 0<α<1 and the Gaussian process Y(t) on ℝ
N
with covariance E(Y(s)Y(t))=|t|2α+|s|2α−|t−s|2α, where |t| is the Euclidean norm of t. Consider independent copies X
1,…,X
d
of Y and␣the process X(t)=(X
1(t),…,X
d
(t)) valued in ℝ
d
. When kN≤␣(k−1)αd, we show that the trajectories of X do not have k-multiple points. If N<αd and kN>(k−1)αd, the set of k-multiple points of the trajectories X is a countable union of sets of finite Hausdorff measure associated with the function ϕ(ɛ)=ɛ
k
N
/α−(
k
−1)
d
(loglog(1/ɛ))
k
. If N=αd, we show that the set of k-multiple points of the trajectories of X is a countable union of sets of finite Hausdorff measure associated with the function ϕ(ɛ)=ɛ
d
(log(1/ɛ) logloglog 1/ɛ)
k
. (This includes the case k=1.)
Received: 20 May 1997 / Revised version: 15 May 1998 相似文献
10.
Michael Talagrand 《Israel Journal of Mathematics》1981,40(3-4):324-330
Letτ be a cardinal with cf(τ)>ℵ0. Then a Banach spaceE contains a subspace isomorphic tol
l(τ) if and only if [0,1]
r
is a continuous image of the unit ballE′1 ofE′, provided with the w*-topology. It follows that, for each cardinalκ, ifE′1 contains a copy ofβκ, thenE has a quotient isomorphic tol
∞(κ). In this situation we show thatE has even a quotientisometric tol
∞(κ).
相似文献
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