Regularite des trajectoires des fonctions aleatoires gaussiennes

Fernique, Xavier

doi:10.1007/bfb0080190

Cited by 352 publications

(303 citation statements)

References 9 publications

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“…This is an extension of Fernique's result to ίJ'-valued processes, (see R. M. Dudley [1] and X. Fernique [2]). …”

Section: J Mξsupporting

confidence: 53%

On the norm continuity of -valued Gaussian processes

Mitoma

1981

Nagoya Mathematical Journal

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SummaryLet Sf be the Schwartz space of all rapidly decreasing functions on R n , Sf 1 be the topological dual space of Sf and for each positive integer p,Sf p be the space of all elements of £f' which are continuous in the p-th norm defining the nuclear Frechet topology of Sf. The main purpose of the present paper is to show that if {X tί t e [0, + oo)} is an ^'-valued Gaussian process and for any fixed φβ^ the real Gaussian process {X t (φ) 9 1 e [0, + oo)} has a continuous version, then for any fixed T > 0 there is a positive integer p such that {X t , t e [0, T]} has a version which is continuous in the norm topology of S?' p .

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“…This is an extension of Fernique's result to ίJ'-valued processes, (see R. M. Dudley [1] and X. Fernique [2]). …”

Section: J Mξsupporting

confidence: 53%

On the norm continuity of -valued Gaussian processes

Mitoma

1981

Nagoya Mathematical Journal

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“…We will need the following two Gaussian comparison inequalities: the Sudakov-Fernique inequality, which compares the expected maximum of Gaussian processes (see, e.g., [13] for a proof), and Slepian's comparison lemma [21], which compares the maximum of Gaussian processes in the sense of "stochastic domination". Lemma 3.2 (Sudakov-Fernique).…”

Section: A Few Gaussian Inequalitiesmentioning

confidence: 99%

“…This is achieved by Fernique's criterion [13]. We quote a version suited to our needs, which follows straightforwardly from the version in [2, Theorem 4.1] by using, as the majorizing measure, the normalized counting measure on B.…”

Section: Lemma 33 (Slepian)mentioning

confidence: 99%

Convergence in Law of the Maximum of the Two‐Dimensional Discrete Gaussian Free Field

Bramson

Ding

Zeitouni

2015

Comm Pure Appl Math

132

259

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“…The upper bound is due to Fernique [17] and the lower bound is Talagrand's majorizing measures theorem [42,44].…”

Section: Definition 21 For a Metric Space (T D) An Admissible Sequmentioning

confidence: 99%

Suprema of Chaos Processes and the Restricted Isometry Property

Krahmer

Mendelson

Rauhut

2014

Comm Pure Appl Math

221

280

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We present a new bound for suprema of a special type of chaos processes indexed by a set of matrices, which is based on a chaining method. As applications we show significantly improved estimates for the restricted isometry constants of partial random circulant matrices and time-frequency structured random matrices. In both cases the required condition on the number m of rows in terms of the sparsity s and the vector length n is m s log 2 s log 2 n.

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Regularite des trajectoires des fonctions aleatoires gaussiennes

Cited by 352 publications

References 9 publications

On the norm continuity of -valued Gaussian processes

On the norm continuity of -valued Gaussian processes

Convergence in Law of the Maximum of the Two‐Dimensional Discrete Gaussian Free Field

Suprema of Chaos Processes and the Restricted Isometry Property

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