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pro vyhledávání: '"Bates, Erik"'
Autor:
Bates, Erik, Sohn, Youngtak
The Potts spin glass is a generalization of the Sherrington--Kirkpatrick (SK) model that allows for spins to take more than two values. Based on a novel synchronization mechanism, Panchenko (2018) showed that the limiting free energy is given by a Pa
Externí odkaz:
http://arxiv.org/abs/2310.06745
We consider i.i.d. first-passage percolation (FPP) on the two-dimensional square lattice, in the critical case where edge-weights take the value zero with probability $1/2$. Critical FPP is unique in that the Euclidean lengths of geodesics are superl
Externí odkaz:
http://arxiv.org/abs/2309.04454
We study the Busemann process of the planar directed polymer model with i.i.d. weights on the vertices of the planar square lattice, both the general case and the solvable inverse-gamma case. We demonstrate that the Busemann process intertwines with
Externí odkaz:
http://arxiv.org/abs/2307.10531
Autor:
Bates, Erik, Sohn, Youngtak
There is a rich history of expressing the limiting free energy of mean-field spin glasses as a variational formula over probability measures on $[0,1]$, where the measure represents the similarity (or "overlap") of two independently sampled spin conf
Externí odkaz:
http://arxiv.org/abs/2109.14791
Autor:
Bates, Erik, Sohn, Youngtak
Publikováno v:
Electron. J. Probab. 27 (2022), paper no. 52
We prove a Parisi formula for the limiting free energy of multi-species spherical spin glasses with mixed $p$-spin interactions. The upper bound involves a Guerra-style interpolation and requires a convexity assumption on the model's covariance funct
Externí odkaz:
http://arxiv.org/abs/2109.14790
Autor:
Bates, Erik
This monograph resolves - in a dense class of cases - several open problems concerning geodesics in i.i.d. first-passage percolation on $\mathbb{Z}^d$. Our primary interest is in the empirical measures of edge-weights observed along geodesics from $0
Externí odkaz:
http://arxiv.org/abs/2006.12580
Autor:
Bates, Erik, Podder, Moumanti
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 processes have focused almost exclusively on complete graphs, in particula
Externí odkaz:
http://arxiv.org/abs/2001.11524
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 arXiv:1812.00309 of Dauvergne, Ortmann, and Vir\'ag, this object was con
Externí odkaz:
http://arxiv.org/abs/1912.04164
Autor:
Bates, Erik
Publikováno v:
Electron. J. Probab. 26 (2021), paper no. 74
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 measure is bounded away from $0$. Nevertheless, the question of where along
Externí odkaz:
http://arxiv.org/abs/1910.12012