10 citations · 23 across the 11 of their papers we have counts for
14 papers
On a general Kac-Rice formula for the measure of a level set
Diego Armentano, Jean-Marc Azaïs, José Rafael León
Let be a random field , . We first studied the level set , . In particular we gave a weak condi…
Random and mean Lyapunov exponents for
Diego Armentano, Gautam Chinta, Siddhartha Sahi +1
We consider orthogonally invariant probability measures on and compare the mean of the logs of the moduli of eigenvalues of the matrices to the Lyapunov…
On the finiteness of the moments of the measure of level sets of random fields
Diego Armentano, Jean-Marc Azaïs, Federico Dalmao +2
General conditions on smooth real valued random fields are given that ensure the finiteness of the moments of the measure of their level sets. As a by product a new generalized Kac…
Conditions for the finiteness of the moments of the volume of level sets
Diego Armentano, Jean-Marc Azais, David Ginsbourger +1
Let X(t) be a Gaussian random field R d R. Using the notion of (d -- 1)-integral geometric measures, we establish a relation between (a) the volume of the level set (…
Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems
Jean-Marc Azaïs, Diego Armentano, Federico Dalmao +1
We state the Central Limit Theorem, as the degree goes to infinity, for the normalized volume of the zero set of a rectangular Kostlan-Shub-Smale random polynomial system. This pap…
Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems
Diego Armentano, Jean-Marc Azaïs, Federico Dalmao +1
We obtain a Central Limit Theorem for the normalized number of real roots of a square Kostlan-Shub-Smale random polynomial system of any size as the degree goes to infinity. A stud…
The polynomial eigenvalue problem is well conditioned for random inputs
Carlos Beltrán, Diego Armentano
We compute the exact value of the squared condition number for the polynomial eigenvalue problem, when the input matrices have entries coming from the standard complex Gaussian dis…
Condition length and complexity for the solution of polynomial systems
Diego Armentano, Carlos Beltrán, Peter Bürgisser +2
Smale's 17th problem asks for an algorithm which finds an approximate zero of polynomial systems in average polynomial time (see Smale 2000). The main progress on Smale's problem i…
Average polynomial time for eigenvector computations
Diego Armentano, Carlos Beltrán, Michael Shub
We describe two algorithms for the eigenvalue, eigenvector problem which, on input a Gaussian matrix with complex entries, finish with probability 1 and in average polynomial time.
Smale's Fundamental Theorem of Algebra reconsidered
Diego Armentano, Michael Shub
In his 1981 Fundamental Theorem of Algebra paper Steve Smale initiated the complexity theory of finding a solution of polynomial equations of one complex variable by a variant of N…
Complexity of Path-Following Methods for the Eigenvalue Problem
Diego Armentano
A unitarily invariant projective framework is introduced to analyze the complexity of path-following methods for the eigenvalue problem. A condition number, and its relation to the…
A review of some recent results on random polynomials over R and over C
Diego Armentano
This article is divided in two parts. In the first part we review some recent results concerning the expected number of real roots of random system of polynomial equations. In the…
Average-Case Perturbations and Smooth Condition Numbers
Diego Armentano
We define a new condition number adapted to directionally uniform perturbations. The definitions and theorems can be applied to a large class of problems. We show the relation with…
Random systems of polynomial equations. The expected number of roots under smooth analysis
Diego Armentano, Mario Wschebor
We consider random systems of equations over the reals, with equations and unknowns , , , where the 's are non-random pol…