24 citations · 89 across the 12 of their papers we have counts for
16 papers
Longest convex chains with i.i.d. points
Erik Bates, Arnab Sen
Sample i.i.d. points from a triangle, according to some continuous density function. Given two vertices of the triangle, what is the maximum number of samples that form a…
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…
Crisanti-Sommers formula and simultaneous symmetry breaking in multi-species spherical spin glasses
Erik Bates, Youngtak Sohn
There is a rich history of expressing the limiting free energy of mean-field spin glasses as a variational formula over probability measures on , where the measure represent…
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…
Empirical Measures, Geodesic Lengths, and a Variational Formula in First-Passage Percolation
Erik Bates
This monograph resolves - in a dense class of cases - several open problems concerning geodesics in i.i.d. first-passage percolation on . Our primary interest is in t…
Avoidance couplings on non-complete graphs
Erik Bates, Moumanti Podder
A coupling of random walkers on the same finite graph, who take turns sequentially, is said to be an avoidance coupling if the walkers never collide. Previous studies of these proc…
Hausdorff dimensions for shared endpoints of disjoint geodesics in the directed landscape
Erik Bates, Shirshendu Ganguly, Alan Hammond
Within the Kardar-Parisi-Zhang universality class, the space-time Airy sheet is conjectured to be the canonical scaling limit for last passage percolation models. In recent work ar…
Full-path localization of directed polymers
Erik Bates
Certain polymer models are known to exhibit path localization in the sense that at low temperatures, the average fractional overlap of two independent samples from the Gibbs measur…
Localization and free energy asymptotics in disordered statistical mechanics and random growth models
Erik Bates
This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechan…
Localization in Gaussian disordered systems at low temperature
Erik Bates, Sourav Chatterjee
For a broad class of Gaussian disordered systems at low temperature, we show that the Gibbs measure is asymptotically localized in small neighborhoods of a small number of states.…
Fluctuation lower bounds in planar random growth models
Erik Bates, Sourav Chatterjee
We prove lower bounds on the order of growth fluctuations in three planar growth models (first-passage percolation, last-passage percolation, and directed polymers)…
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…
An upper bound on the size of avoidance couplings
Erik Bates, Lisa Sauermann
We show that a coupling of non-colliding simple random walkers on the complete graph on vertices can include at most walkers. This improves the only previously kno…
Localization of directed polymers with general reference walk
Erik Bates
Directed polymers in random environment have usually been constructed with a simple random walk on the integer lattice. It has been observed before that several standard results fo…
The endpoint distribution of directed polymers
Erik Bates, Sourav Chatterjee
Probabilistic models of directed polymers in random environment have received considerable attention in recent years. Much of this attention has focused on integrable models. In th…
Inverse Modeling of Dynamical Systems: Multi-Dimensional Extensions of a Stochastic Switching Problem
Erik Bates, Blake Chamberlain, Rachel Gettinger
The Buridan's ass paradox is characterized by perpetual indecision between two states, which are never attained. When this problem is formulated as a dynamical system, indecision i…