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- Interdisciplinary Centre for Security, Reliability and TrustLU193 papers
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124 papers · 1 filter
Expected Lipschitz-Killing curvatures for spin random fields and other non-isotropic fields
Francesca Pistolato, Michele Stecconi
Spherical spin random fields are used to model the Cosmic Microwave Background polarization, the study of which is at the heart of modern Cosmology and will be the subject of the L…
Limit theorems for -domain functionals of stationary Gaussian fields
Nikolai Leonenko, Leonardo Maini, Ivan Nourdin +1
Fix an integer and refer to it as the number of growing domains. For each , fix a compact subset where $d_1,\ldots,d_p\g…
Length spectrum of large genus random metric maps
Simon Barazer, Alessandro Giacchetto, Mingkun Liu
We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichmüller theory approach. We establish that, as the genu…
Functional Convergence of Berry's Nodal Lengths: Approximate Tightness and Total Disorder
Massimo Notarnicola, Giovanni Peccati, Anna Vidotto
We consider Berry's random planar wave model (1977), and prove spatial functional limit theorems - in the high-energy limit - for discretized and truncated versions of the random f…
Instance-dependent uniform tail bounds for empirical processes
Sohail Bahmani
We formulate a uniform tail bound for empirical processes indexed by a class of functions, in terms of the individual deviations of the functions rather than the worst-case deviati…
Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds
Qin-Qian Chen, Li-Juan Cheng, Anton Thalmaier
In this article, we develop a martingale approach to localized Bismut-type Hessian formulas for heat semigroups on Riemannian manifolds. Our approach extends the Hessian formulas e…