Franco Severo

activity

20182026

most citedEquality of critical parameters for percolation of Gaussian free field level-sets

54 citations · 125 across the 18 of their papers we have counts for

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21 papers · 1 filter

math.PR2026

Weighted isoperimetry implies percolation

Ivailo Hartarsky, Franco Severo, Augusto Teixeira

Consider an infinite edge-weighted graph satisfying an isoperimetric inequality of the type $∥ \partial A ∥ \geq C ∣ A ∣^{α}$ for some $α, C > 0$ , where $∥ \partial A ∥$ denotes the weighte…

math.PR2026

Supercritical sharpness for the random cluster representation of real-valued spin models

Trishen S. Gunaratnam, Dmitry Krachun, Christoforos Panagiotis +2

We study the supercritical regime $β > β_{c}$ of a large family of real-valued spin models on $Z^{d}$ , including the Blume-Capel and $P (φ)$ models. We consider their random clust…

math.PR2025

High-intensity Voronoi percolation on manifolds

Tillmann Bühler, Barbara Dembin, Ritvik Ramanan Radhakrishnan +1

We study Voronoi percolation on a large class of $d$ -dimensional Riemannian manifolds, which includes the hyperbolic spaces $H^{d}$ , $d \geq 2$ . We prove that as the intensit…

math.PR2025

The supercritical phase of the $φ^{4}$ model is well behaved

Trishen S. Gunaratnam, Christoforos Panagiotis, Romain Panis +1

In this article, we analyse the $φ^{4}$ model on $Z^{d}$ in the supercritical regime $β > β_{c}$ . We consider a random cluster representation of the $φ^{4}$ model, which corresponds…

math.PR2024

Percolation on the stationary distributions of the voter model with stirring

Jhon Astoquillca, Franco Severo, Réka Szabó +1

The voter model with stirring is a variant of the classical voter model on $Z^{d}$ with two possible opinions (0 and 1) that, in addition to copying neighbouring opinions at…

math.PR2024★ 1 cited

Counting minimal cutsets and $p_{c} < 1$

Philip Easo, Franco Severo, Vincent Tassion

We prove two results concerning percolation on general graphs. - We establish the converse of the classical Peierls argument: if the critical parameter for (uniform) percolation sa…

math.PR2023

Slab percolation for the Ising model revisited

Franco Severo

In this note, we give a new and short proof for a theorem of Bodineau stating that the slab percolation threshold $p^_{c}$ for the FK-Ising model coincides with the standard per…

math.PR2023

Supercritical sharpness for Voronoi percolation

Barbara Dembin, Franco Severo

We prove that the supercritical phase of Voronoi percolation on $R^{d}$ , $d \geq 3$ , is well behaved in the sense that for every $p > p_{c} (d)$ local uniqueness of macroscopic cl…

math.PR2023

A characterization of strong percolation via disconnection

Hugo Duminil-Copin, Subhajit Goswami, Pierre-François Rodriguez +2

We consider a percolation model, the vacant set $V^{u}$ of random interlacements on $Z^{d}$ , $d \geq 3$ , in the regime of parameters $u > 0$ in which it is strongly pe…

math.PR2023

Phase transition for the vacant set of random walk and random interlacements

Hugo Duminil-Copin, Subhajit Goswami, Pierre-François Rodriguez +2

We consider the set of points visited by the random walk on the discrete torus $(Z / N Z)^{d}$ , for $d \geq 3$ , at times of order $u N^{d}$ , for a parameter $u > 0$ in the…

math.PR2023

Finite range interlacements and couplings

Hugo Duminil-Copin, Subhajit Goswami, Pierre-François Rodriguez +2

In this article, we consider the interlacement set $I^{u}$ at level $u > 0$ on $Z^{d}$ , $d \geq 3$ , and its finite range version $I^{u, L}$ for $L > 0$ , given b…

math.PR2022★ 1 cited

Random tangled currents for $φ^{4}$ : translation invariant Gibbs measures and continuity of the phase transition

Trishen S. Gunaratnam, Christoforos Panagiotis, Romain Panis +1

We prove that the set of automorphism invariant Gibbs measures for the $φ^{4}$ model on graphs of polynomial growth has at most two extremal measures at all values of $β$ . We also gi…

math.PR2022

Uniqueness of unbounded component for level sets of smooth Gaussian fields

Franco Severo

For a large family of stationary continuous Gaussian fields $f$ on $R^{d}$ , including the Bargmann-Fock and Cauchy fields, we prove that there exists at most one unbounded c…

math.PR2022★ 6 cited

Percolation of strongly correlated Gaussian fields I. Decay of subcritical connection probabilities

Stephen Muirhead, Franco Severo

We study the decay of connectivity of the subcritical excursion sets of a class of strongly correlated Gaussian fields. Our main result shows that, for smooth isotropic Gaussian fi…

math.PR2021

Gap at 1 for the percolation threshold of Cayley graphs

Christoforos Panagiotis, Franco Severo

We prove that the set of possible values for the percolation threshold $p_{c}$ of Cayley graphs has a gap at 1 in the sense that there exists $ε_{0} > 0$ such that for every Ca…

math.PR2021★ 7 cited

Analyticity of Gaussian free field percolation observables

Christoforos Panagiotis, Franco Severo

We prove that cluster observables of level-sets of the Gaussian free field on the hypercubic lattice $Z^{d}$ , $d \geq 3$ , are analytic on the whole off-critical regime $\mathb…

math.PR2021

Sharp phase transition for Gaussian percolation in all dimensions

Franco Severo

We consider the level-sets of continuous Gaussian fields on $R^{d}$ above a certain level $- ℓ \in R$ , which defines a percolation model as $ℓ$ varies. We assum…

math.PR2021★ 27 cited

On the radius of Gaussian free field excursion clusters

Subhajit Goswami, Pierre-François Rodriguez, Franco Severo

We consider the Gaussian free field $φ$ on $Z^{d}$ , for $d \geq 3$ , and give sharp bounds on the probability that the radius of a finite cluster in the excursion set $\{φ\geq…

math.PR2020★ 54 cited

Equality of critical parameters for percolation of Gaussian free field level-sets

Hugo Duminil-Copin, Subhajit Goswami, Pierre-François Rodriguez +1

We consider upper level-sets of the Gaussian free field on $Z^{d}$ , for $d \geq 3$ , above a given real-valued height parameter $h$ . As $h$ varies, this defines a canonical per…

math.PR2018★ 29 cited

Existence of phase transition for percolation using the Gaussian Free Field

Hugo Duminil-Copin, Subhajit Goswami, Aran Raoufi +2

In this paper, we prove that Bernoulli percolation on bounded degree graphs with isoperimetric dimension $d > 4$ undergoes a non-trivial phase transition (in the sense that $p_{c} < 1$ ).…

math.PR2018

Strict monotonicity of percolation thresholds under covering maps

Sébastien Martineau, Franco Severo

We answer a question of Benjamini and Schramm by proving that under reasonable conditions, quotienting a graph strictly increases the value of its percolation critical parameter $p…

Weighted isoperimetry implies percolation

Supercritical sharpness for the random cluster representation of real-valued spin models

High-intensity Voronoi percolation on manifolds

The supercritical phase of the φ4 model is well behaved

Percolation on the stationary distributions of the voter model with stirring

Counting minimal cutsets and pc​<1

Slab percolation for the Ising model revisited

Supercritical sharpness for Voronoi percolation

A characterization of strong percolation via disconnection

Phase transition for the vacant set of random walk and random interlacements

Finite range interlacements and couplings

Random tangled currents for φ4: translation invariant Gibbs measures and continuity of the phase transition

Uniqueness of unbounded component for level sets of smooth Gaussian fields

Percolation of strongly correlated Gaussian fields I. Decay of subcritical connection probabilities

Gap at 1 for the percolation threshold of Cayley graphs

Analyticity of Gaussian free field percolation observables

Sharp phase transition for Gaussian percolation in all dimensions

On the radius of Gaussian free field excursion clusters

Equality of critical parameters for percolation of Gaussian free field level-sets

Existence of phase transition for percolation using the Gaussian Free Field

Strict monotonicity of percolation thresholds under covering maps

The supercritical phase of the $φ^{4}$ model is well behaved

Counting minimal cutsets and $p_{c} < 1$

Random tangled currents for $φ^{4}$ : translation invariant Gibbs measures and continuity of the phase transition