125 citations · 749 across the 10 of their papers we have counts for
10 papers
Critical Behaviour of the Number of Minima of a Random Landscape at the Glass Transition Point and the Tracy-Widom distribution
Yan V. Fyodorov, Celine Nadal
We exploit a relation between the mean number of minima of random Gaussian surfaces and extreme eigenvalues of random matrices to understand the critical behaviour of $N_{m…
Right tail expansion of Tracy-Widom beta laws
Gaëtan Borot, Céline Nadal
Using loop equations, we compute the large deviation function of the maximum eigenvalue to the right of the spectrum in the Gaussian beta matrix ensembles, to all orders in 1/N. We…
Purity distribution for generalized random Bures mixed states
Gaëtan Borot, Céline Nadal
We compute the distribution of the purity for random density matrices (i.e.random mixed states) in a large quantum system, distributed according to the Bures measure. The full dist…
A simple derivation of the Tracy-Widom distribution of the maximal eigenvalue of a Gaussian unitary random matrix
Celine Nadal, Satya N. Majumdar
In this paper, we first briefly review some recent results on the distribution of the maximal eigenvalue of a random matrix drawn from Gaussian ensembles. Next we foc…
How many eigenvalues of a Gaussian random matrix are positive?
Satya N. Majumdar, Céline Nadal, Antonello Scardicchio +1
We study the probability distribution of the index , i.e., the number of positive eigenvalues of an Gaussian random matrix. We show analytically that, f…
Large deviations of the maximal eigenvalue of random matrices
Gaëtan Borot, Bertrand Eynard, Satya N. Majumdar +1
We present detailed computations of the 'at least finite' terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in beta-ensembles, with any…
Statistical distribution of quantum entanglement for a random bipartite state
Celine Nadal, Satya N Majumdar, Massimo Vergassola
We compute analytically the statistics of the Renyi and von Neumann entropies (standard measures of entanglement), for a random pure state in a large bipartite quantum system. The…
Phase Transitions in the Distribution of Bipartite Entanglement of a Random Pure State
Celine Nadal, Satya N. Majumdar, Massimo Vergassola
Using a Coulomb gas method, we compute analytically the probability distribution of the Renyi entropies (a standard measure of entanglement) for a random pure state of a large bipa…
The Index Distribution of Gaussian Random Matrices
Satya N. Majumdar, Celine Nadal, Antonello Scardicchio +1
We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (…
Non-intersecting Brownian Interfaces and Wishart Random Matrices
Céline Nadal, Satya N. Majumdar
We study a system of non-intersecting -dimensional fluctuating elastic interfaces (`vicious bridges') at thermal equilibrium, each subject to periodic boundary condition…