4 papers · 1 filter
Renormalization of crossing probabilities in the dilute Potts model
Pete Rigas
A recent paper due to Duminil-Copin and Tassion from 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
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,…
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…
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 , relating to level-set percolation on metric-graphs for the G…