Level Sets and Extrema of Random Processes and Fields

By Jean-Marc Azaïs, Mario Wschebor. 2009

617 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4fd97d99efb46047d542b946c0b19b1b38028b59

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In Statistical and Nonlinear Physics

1. École d'été de probabilités de Saint-Flour
2. José Rafael León
3. Domenico Marinucci
4. Jirí Cerný
5. Jonathan E. Taylor
6. Anne Estrade
7. Holger Rauhut
8. Robert J. Adler

Citations in the corpus

• A Confidence Corridor for Sparse Longitudinal Data Curves (2011, neutral): “…= η (s) = u ] ≤ E [ {η′ (t)}2 |η (t) = η (s) = u ] ≤ E2 {η′ (t) |η (t) = η (s) = u}+ Var {η′ (t) |η (t) = η (s) = u} , E {η′ (t) |η (t) = η (s) = u} = r1,0 (t, s)u/ (1 + r) , (A.33) Var {η′ (t) |η (t) = η (s) = u} = r1,1 (t, t)− r21,0 (t, s) / ( 1− r2 ) , (A.34) see Azäıs and Wschebor (2009) p.96.”
• A quantitative central limit theorem for the Euler–Poincaré characteristic of random spherical eigenfunctions (2016, positive): “Under Condition 3, we can apply Kac–Rice formula to compute E[μj(ε)μk(ε)] (see [3], Theorem 6.”
• Extreme Value Analysis: an Introduction (2013, background): “In addition, Adler (2000) and Azaïs and Wschebor (2009) are mainly dedicated to level sets and extrema of Gaussian random fields.”
• Compressive Sensing with structured random matrices (2012, methodology): “Although we will need Dudley’s inequality only for Rademacher processes here, we note that the original formulation was for Gaussian processes, see also [3, 79, 80, 99, 125].”
• Random Matrices and Complexity of Spin Glasses (2010, methodology): “These formulas are consequences of the classical Kac-Rice formula (see [AT07] and [AW09] for two excellent recent books giving a very complete account of this formula and its consequences).”
• Topological complexity of smooth random functions (2011, background): “Since we shall not need this result in what follows, we send you to RFG or [11] for further details.”
• A central limit theorem for the Euler characteristic of a Gaussian excursion set (2016, methodology): “Many authors were and still are interested in this domain as proved by the successful books of Adler and Taylor [5] and Azaïs and Wshebor [12], or the recent papers [9, 13, 23, 30], among others.”