Alejandro Rivera

activity

20162021

most citedThe phase transition for planar Gaussian percolation models without FKG

4 citations · 8 across the 9 of their papers we have counts for

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9 papers · 1 filter

math.PR2021★ 1 cited

Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension $d \geq 3$

Hugo Duminil-Copin, Alejandro Rivera, Pierre-François Rodriguez +1

For the Bargmann--Fock field on $R^{d}$ with $d \geq 3$ , we prove that the critical level $ℓ_{c} (d)$ of the percolation model formed by the excursion sets ${f \geq ℓ}$ is…

math.PR2021

On the limiting behaviour of arithmetic toral eigenfunctions

Riccardo W. Maffucci, Alejandro Rivera

We consider a wide class of families $(F_{m})_{m \in N}$ of Gaussian fields on $T^{d} = R^{d} / Z^{d}$ defined by \[F_m:x\mapsto \frac{1}{\sqrt{|Λ_m|}}\sum_{λ…

math.PR2020★ 4 cited

The phase transition for planar Gaussian percolation models without FKG

Stephen Muirhead, Alejandro Rivera, Hugo Vanneuville +1

We develop techniques to study the phase transition for planar Gaussian percolation models that are not (necessarily) positively correlated. These models lack the property of posit…

math.PR2019

Talagrand's inequality in planar Gaussian field percolation

Alejandro Rivera

Let f be a stationary isotropic non-degenerate Gaussian field on R^2. Assume that f = q * W where q is both C^2 and L^2 and W is the L^2 white noise on R^2. We extend a result by S…

math.PR2018

A covariance formula for topological events of smooth Gaussian fields

Dmitry Beliaev, Stephen Muirhead, Alejandro Rivera

We derive a covariance formula for the class of `topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of…

math.PR2018★ 3 cited

Expected number of nodal components for cut-off fractional Gaussian fields

Alejandro Rivera

Let $(X, g)$ be a closed Riemmanian manifold of dimension $n > 0$ . Let $Δ$ be the Laplacian on $X$ , and let $(e_k)_k$ be an $L^{2}$ -orthonormal and dense famil…

math.PR2017

The critical threshold for Bargmann-Fock percolation

Alejandro Rivera, Hugo Vanneuville

In this article, we study the excursions sets $D_p = f^{- 1} ([- p, + \infty [)$ where $f$ is a natural real-analytic planar Gaussian field called the Bargmann-Fock field. More…

math.PR2017

Quasi-independence for nodal lines

Alejandro Rivera, Hugo Vanneuville

We prove a quasi-independence result for level sets of a planar centered stationary Gaussian field with covariance $(x, y) \mapsto κ (x - y)$ . As a first application, we study percolatio…

math.PR2016

Hole probability for nodal sets of the cut-off Gaussian Free Field

Alejandro Rivera

Let ( $Σ$ , g) be a closed connected surface equipped with a riemannian metric. Let ( $λ$ n) n $\in$ N and ( $ψ$ n) n $\in$ N be the increasing sequence of eigenvalues and the sequence of…

Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension d≥3

On the limiting behaviour of arithmetic toral eigenfunctions

The phase transition for planar Gaussian percolation models without FKG

Talagrand's inequality in planar Gaussian field percolation

A covariance formula for topological events of smooth Gaussian fields

Expected number of nodal components for cut-off fractional Gaussian fields

The critical threshold for Bargmann-Fock percolation

Quasi-independence for nodal lines

Hole probability for nodal sets of the cut-off Gaussian Free Field

Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension $d \geq 3$