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4 papers · 2 filters
Osculating Random Walks on Cylinders
Saibal Mitra, Bernard Nienhuis
We consider random paths on a square lattice which take a left or a right turn at every vertex. The possible turns are taken with equal probability, except at a vertex which has be…
A Guide to Stochastic Loewner Evolution and its Applications
Wouter Kager, Bernard Nienhuis
This article is meant to serve as a guide to recent developments in the study of the scaling limit of critical models. These new developments were made possible through the definit…
Exact Solutions for Loewner Evolutions
Wouter Kager, Bernard Nienhuis, Leo P. Kadanoff
In this note, we solve the Loewner equation in the upper half-plane with forcing function xi(t), for the cases in which xi(t) has a power-law dependence on time with powers 0, 1/2…
Expansions about Free-Fermion Models
Saibal Mitra
A simple technique for expanding the free energy of general six-vertex models about free-fermion points is introduced. This technique is used to verify a Coulomb gas prediction abo…