Pete Rigas

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20212026

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math.PR2023

Scaling limit of the triangular kinetic prudent walk

Pete Rigas

Expressions for scaling limits of random walks, such as those obtained in several areas of the Probability theory literature, are of great significance in characterizing long term,…

math.PR2023

Operator formalism for discretely holomorphic parafermions of the two-color Ashkin-Teller, loop $O (1)$ , staggered eight-vertex, odd eight-vertex, and abelian sandpile models

Pete Rigas

We extend an operator formalism, developed by Hongler, Kytölä, and Zahabi in 2012 for the Ising model, to the Ashkin-Teller and loop $O (n)$ models. The formalism is pr…

math.PR2023

Phase transition of the long range Ising model in lower dimensions, for $d < α \leq d + 1$ , with a Peierls argument

Pete Rigas

We extend previous results due to Ding and Zhuang in order to prove that a phase transition occurs for the long range Ising model in lower dimensions. By making use of a recent arg…

math.PR2023

The phase transition for the Gaussian free field is sharp

Pete Rigas

We prove that the phase transition for the Gaussian free field (GFF) is sharp. In comparison to a previous argument due to Rodriguez in 2017 which characterized a $0 - 1$ law for the…

math.PR2022

Kesten's incipient infinite cluster for the three-dimensional, metric-graph Gaussian free field, from critical level-set percolation, and for the Villain model, from random cluster geometries and a Swendsen-Wang type algorithm

Pete Rigas

We address one open problem in a recent work due to Ding and Wirth, the first version of which was available in $2019$ , relating to level-set percolation on metric-graphs for the G…

math.PR2022

Correlation length lower bound for the random-field Potts model with the greedy lattice animal

Pete Rigas

Motivated by recent developments over the past few years in the study of the correlation length of the random-field Ising model due to Ding and Wirth in a paper first available in…

math.PR2022

From logarithmic delocalization of the six-vertex height function under sloped boundary conditions to weakened crossing probability estimates for the Ashkin-Teller, generalized random-cluster, and $(q_{σ}, q_{τ})$ -cubic models

Pete Rigas

To obtain Russo-Seymour-Welsh estimates for the height function of the six-vertex model under sloped boundary conditions, which can be leveraged to demonstrate that the height func…

math.PR2021

Renormalization of crossing probabilities in the dilute Potts model

Pete Rigas

A recent paper due to Duminil-Copin and Tassion from $2019$ introduces a novel argument for obtaining estimates on horizontal crossing probabilities of the Random-Cluster model, in…

Scaling limit of the triangular kinetic prudent walk

Operator formalism for discretely holomorphic parafermions of the two-color Ashkin-Teller, loop O(1), staggered eight-vertex, odd eight-vertex, and abelian sandpile models

Phase transition of the long range Ising model in lower dimensions, for d<α≤d+1, with a Peierls argument

The phase transition for the Gaussian free field is sharp

Kesten's incipient infinite cluster for the three-dimensional, metric-graph Gaussian free field, from critical level-set percolation, and for the Villain model, from random cluster geometries and a Swendsen-Wang type algorithm

Correlation length lower bound for the random-field Potts model with the greedy lattice animal

From logarithmic delocalization of the six-vertex height function under sloped boundary conditions to weakened crossing probability estimates for the Ashkin-Teller, generalized random-cluster, and (qσ​,qτ​)-cubic models

Renormalization of crossing probabilities in the dilute Potts model

Operator formalism for discretely holomorphic parafermions of the two-color Ashkin-Teller, loop $O (1)$ , staggered eight-vertex, odd eight-vertex, and abelian sandpile models

Phase transition of the long range Ising model in lower dimensions, for $d < α \leq d + 1$ , with a Peierls argument

From logarithmic delocalization of the six-vertex height function under sloped boundary conditions to weakened crossing probability estimates for the Ashkin-Teller, generalized random-cluster, and $(q_{σ}, q_{τ})$ -cubic models