3 papers
math.PR2023
Quantitative sub-ballisticity of self-avoiding walk on the hexagonal lattice
Dmitrii Krachun, Christoforos Panagiotis
We prove quantitative sub-ballisticity for the self-avoiding walk on the hexagonal lattice. Namely, we show that with high probability a self-avoiding walk of length does not e…
math.PR2023
Scaling limit of the cluster size distribution for the random current measure on the complete graph
Dmitrii Krachun, Christoforos Panagiotis, Romain Panis
We study the percolation configuration arising from the random current representation of the near-critical Ising model on the complete graph. We compute the scaling limit of the cl…
math.CO2023
Strong greedoid structure of -removed -orderings
Dmitrii Krachun, Rozalina Mirgalimova
Inspired by the notion of \emph{-removed -orderings} introduced in the setting of Dedekind domains by Bhargava \cite{Bha09-1} we study its generalization in the framework of…