4 papers · 1 filter
Longest convex chains with i.i.d. points
Erik Bates, Arnab Sen
Sample i.i.d. points from a triangle, according to some bounded density function. Given two vertices of the triangle, what is the maximum number of samples that form a co…
Free energy in multi-species mixed -spin spherical models
Erik Bates, Youngtak Sohn
We prove a Parisi formula for the limiting free energy of multi-species spherical spin glasses with mixed -spin interactions. The upper bound involves a Guerra-style interpolati…
Replica symmetry breaking in multi-species Sherrington-Kirkpatrick model
Erik Bates, Leila Sloman, Youngtak Sohn
In the Sherrington-Kirkpatrick (SK) and related mixed -spin models, there is interest in understanding replica symmetry breaking at low temperatures. For this reason, the so-cal…
Intertwining the Busemann process of the directed polymer model
Erik Bates, Wai-Tong Louis Fan, Timo Seppäläinen
We study the Busemann process and competition interfaces of the planar directed polymer model with i.i.d.\ weights on the vertices of the planar square lattice, in both the general…