9 papers · 1 filter
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,…
Optimal, and approximately optimal, quantum strategies for and games
Pete Rigas
We analyze optimal, and approximately optimal, quantum strategies in two non-local settings based upon previous investigations of the XOR and CHSH games. By building upon previous…
Open boundary conditions of the spin chain and sectors of conformal field theories
Pete Rigas
We study open boundary conditions for the spin chain, which shares connections with the six-vertex model, under staggering, and also to the antiferromagnetic Potts mode…
Poisson structure and Integrability of a Hamiltonian flow for the inhomogeneous six-vertex model
Pete Rigas
We compute the action-angle variables for a Hamiltonian flow of the inhomogeneous six-vertex model, from a formulation introduced in a 2022 work due to Keating, Reshetikhin, and Sr…
Operator formalism for discretely holomorphic parafermions of the two-color Ashkin-Teller, loop , 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 models. The formalism is pr…
Eigenvalue attraction in open quantum systems, biophysical systems, and Parity-Time symmetric materials
Pete Rigas
We investigate eigenvalue attraction for open quantum systems, biophysical systems, and for Parity-Time symmetric materials. To determine whether an eigenvalue and its complex conj…
Phase transition of the long range Ising model in lower dimensions, for , 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…
Eigenvectors of Toeplitz matrices from Fisher-Hartwig symbols with greater than, or equal to, one singularity
Pete Rigas
Asymptotically, we analytically derive the form of eigenvectors for two Fisher-Hartwig symbols besides those which were previously investigated in a work due to Movassagh an…
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 law for the…