17 citations · 72 across the 19 of their papers we have counts for
20 papers
Unimodular Zeros of Selmer's Harmonic Trinomials
Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete
Let be positive integers and let . In this note, we classify the unimodular zeros of the harmonic trinomial $H_{\varepsilon,δ}:\mathbb{C}\to \mathbb…
-cut-off phenomenon for Galerkin projections of Fokker-Planck equations with monomial potentials
Benny Avelin, Gerardo Barrera
In this manuscript, we establish the existence/non-existence of the cut-off phenomenon for the Langevin--Kolmogorov random dynamics with monomial convex potentials, possible singul…
Egerváry's theorems for harmonic trinomials
Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete
In this manuscript, we study the arrangements of the roots in the complex plane for the lacunary harmonic polynomials called harmonic trinomials. We provide necessary and sufficien…
Ergodicity bounds for stable Ornstein-Uhlenbeck systems in Wasserstein distance with applications to cutoff stability
Gerardo Barrera, Michael A. Högele
This article establishes cutoff stability also known as abrupt thermalization for generic multidimensional Hurwitz stable Ornstein-Uhlenbeck systems with (possibly degenerate) Lévy…
The stability region for Schur stable trinomials with general complex coefficients
Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete
In this paper, we characterize the stability region for trinomials of the form , , where , and are non-zero complex numbers and $n…
Gradual convergence for Langevin dynamics on a degenerate potential
Gerardo Barrera, Conrado da Costa, Milton Jara
In this paper, we study an ordinary differential equation with a degenerate global attractor at the origin, to which we add a white noise with a small parameter that regulates its…
Quantitative control of Wasserstein distance between Brownian motion and the Goldstein--Kac telegraph process
Gerardo Barrera, Jani Lukkarinen
In this manuscript, we provide a non-asymptotic process level control between the telegraph process and the Brownian motion with suitable diffusivity constant via a Wasserstein dis…
On the number of roots for harmonic trinomials
Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete
In this manuscript we study the counting problem for harmonic trinomials of the form , where , , and , and are non-zero com…
The asymptotic distribution of the condition number for random circulant matrices
Gerardo Barrera, Paulo Manrique-Mirón
In this manuscript, we study the limiting distribution for the joint law of the largest and the smallest singular values for random circulant matrices with generating sequence give…
The cutoff phenomenon in Wasserstein distance for nonlinear stable Langevin systems with small Lévy noise
Gerardo Barrera, Michael A. Högele, Juan Carlos Pardo
This article establishes the cutoff phenomenon in the Wasserstein distance for systems of nonlinear ordinary differential equations with a unique coercive stable fixed point subjec…
The cutoff phenomenon for the stochastic heat and the wave equation subject to small Lévy noise
G. Barrera, M. A. Högele, J. C. Pardo
This article generalizes the small noise cutoff phenomenon to the strong solutions of the stochastic heat equation and the damped stochastic wave equation over a bounded domain sub…
The cutoff phenomenon in total variation for nonlinear Langevin systems with small layered stable noise
G. Barrera, Michael A. Högele, J. C. Pardo
This paper provides an extended case study of the cutoff phenomenon for a prototypical class of nonlinear Langevin systems with a single stable state perturbed by an additive pure…
Cutoff thermalization for Ornstein-Uhlenbeck systems with small Lévy noise in the Wasserstein distance
Gerardo Barrera, Michael A. Högele, Juan Carlos Pardo
This article establishes cutoff thermalization (also known as the cutoff phenomenon) for a class of generalized Ornstein-Uhlenbeck systems wit…
Limit behavior of the invariant measure for Langevin dynamics
Gerardo Barrera
In this manuscript, we consider the Langevin dynamics on with an overdamped vector field and driven by multiplicative Brownian noise of small amplitude , $ε>…
Cut-off phenomenon for the maximum of a sampling of Ornstein-Uhlenbeck processes
Gerardo Barrera
In this article we study the so-called cut-off phenomenon in the total variation distance when for the family of continuous-time stochastic processes indexed by $n\in…
Cut-off phenomenon for Ornstein-Uhlenbeck processes driven by Lévy processes
Gerardo Barrera, Juan Carlos Pardo
In this paper, we study the cut-off phenomenon under the total variation distance of -dimensional Ornstein-Uhlenbeck processes which are driven by Lévy processes. That is to say…
A switch convergence for a small perturbation of a linear recurrence equation
Gerardo Barrera, Shuo Liu
In this article we study a small random perturbation of a linear recurrence equation. If all the roots of its corresponding characteristic equation have modulus strictly less than…
Zero-free neighborhood around the unit circle for Kac polynomials
Gerardo Barrera, Paulo Manrique
In this paper, we study how the roots of the so-called Kac polynomial are concentrating to the unit circle when its coefficients of are in…
Salem-Zygmund Inequality for locally sub-Gaussian random variables, random trigonometric polynomials, and random circulant matrices
Gerardo Barrera, Paulo Manrique
In this manuscript we give an extension of the classic Salem--Zygmund inequality for locally sub-Gaussian random variables. As an application, the concentration of the roots of a K…
Thermalisation for Small Random Perturbations of Dynamical Systems
Gerardo Barrera, Milton Jara
We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditio…