Pete Rigas

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20212026

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Showing 2023 · math.PRShow all

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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…

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

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