66 citations · 258 across the 53 of their papers we have counts for
18 papers · 1 filter
On random Binomial-Fibonacci sequences
Bernard Bercu, Fabrice Gamboa
Motivated by the pioneer work of Viswanath \cite{VIS2000} on random Fibonacci sequences and the development of random Euclidean addition chains in cryptography, we introduce a new…
Sum rules via large deviations: polynomial potentials and multi-cut regime on the unit circle
Fabrice Gamboa, Jan Nagel, Alain Rouault
Sum rules are elegant formulas that relate entropy functionals to coefficients associated with orthogonal polynomials [Sim11]. In a series of paper (see for example [GNR16], [GNR17…
On some gateways between sum rules
Fabrice Gamboa, Jan Nagel, Alain Rouault
We present correspondences induced by some classical mappings between measures on an interval and measures on the unit circle. More precisely, we link their sequences of orthogonal…
Sum rules via large deviations: extension to polynomial potentials and the multi-cut regime
Fabrice Gamboa, Jan Nagel, Alain Rouault
A sum rule is an identity connecting the entropy of a measure with coefficients involved in the construction of its orthogonal polynomials (Jacobi coefficients). Our paper is an ex…
Optimization Of Quasi-convex Function Over Product Measure Sets
Jerome Stenger, Fabrice Gamboa, Merlin Keller
We consider a generalization of the Bauer maximum principle. We work with tensorial products of convex measures sets, that are non necessarily compact but generated by their extrem…
Sum rules and large deviations for spectral matrix measures in the Jacobi ensemble
Fabrice Gamboa, Jan Nagel, Alain Rouault
We continue to explore the connections between large deviations for objects coming from random matrix theory and sum rules. This connection was established in [17] for spectral mea…
Addendum to " Sum rules via large deviations "
Fabrice Gamboa, Jan Nagel, Alain Rouault
In these notes we fill a gap in a proof in Section 4 of Gamboa, Nagel, Rouault [Sum rules via large deviations, J. Funct. Anal. 270 (2016), 509-559]. We prove a general theorem whi…
Sum rules and large deviations for spectral measures on the unit circle
Fabrice Gamboa, Jan Nagel, Alain Rouault
This work is a companion paper of Gamboa, Nagel, Rouault (J. Funct. Anal. 2016). We continue to explore the connections between large deviations for random objects issued from rand…
Sum rules and large deviations for spectral matrix measures
Fabrice Gamboa, Jan Nagel, Alain Rouault
A sum rule relative to a reference measure on R is a relationship between the reversed Kullback-Leibler divergence of a positive measure on R and some non-linear functional built o…
Sensitivity analysis based on Cram{é}r von Mises distance
Fabrice Gamboa, Thierry Klein, Agnès Lagnoux
In this paper, we first study a new sensitivity index that is based on higher moments and generalizes the so-called Sobol one. Further, following an idea of Borgonovo ([3]), we def…
Sum rules via large deviations
Fabrice Gamboa, Jan Nagel, Alain Rouault
In this paper, a sum rule means a relationship between a functional defined on a subset of all probability measures on involving the reverse Kullback-Leibler divergenc…
Operator-valued spectral measures and large deviations
Fabrice Gamboa, Alain Rouault
We study large deviation properties of random matricial spectral measures.
Large Deviations for Random Matricial Moment Problems
Fabrice Gamboa, Jan Nagel, Alain Rouault +1
We consider the moment space corresponding to complex matrix measures defined on ( or $K=\D$). We endow this set with the uniform law.…
Generalized Dirichlet distributions on the ball and moments
Franck Barthe, Fabrice Gamboa, Li-Vang Lozada-Chang +1
The geometry of unit -dimensional balls has been intensively investigated in the past decades. A particular topic of interest has been the study of the asymptotics of…
Large Deviations for Random Spectral Measures and Sum Rules
Fabrice Gamboa, Alain Rouault
We prove a Large Deviation Principle for the random spec- tral measure associated to the pair where is sampled in the GUE(N) and e is a fixed unit vector (and more…
Canonical moments and random spectral measures
Fabrice Gamboa, Alain Rouault
We study some connections between the random moment problem and the random matrix theory. A uniform draw in a space of moments can be lifted into the spectral probability measure o…
Conditional large and moderate deviations for sums of discrete random variables. Combinatoric applications
Fabrice Gamboa, Thierry Klein, Clémentine Prieur
We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some application…
Large Deviations for Random Power Moment Problem
Fabrice Gamboa, Li-Vang Lozada-Chang
We consider the set M_n of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in M_n,…