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9 papers · 2 filters
Random Overlap Structures: Properties and Applications to Spin Glasses
Louis-Pierre Arguin, Sourav Chatterjee
Random Overlap Structures (ROSt's) are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by…
The large deviation principle for the Erdős-Rényi random graph
Sourav Chatterjee, S. R. S. Varadhan
What does an Erdos-Renyi graph look like when a rare event happens? This paper answers this question when p is fixed and n tends to infinity by establishing a large deviation princ…
A note on the invariant distribution of a quasi-birth-and-death process
Manuel D. de la Iglesia
The aim of this paper is to give an explicit formula of the invariant distribution of a quasi-birth-and-death process in terms of the block entries of the transition probability ma…
Crossover distributions at the edge of the rarefaction fan
Ivan Corwin, Jeremy Quastel
We consider the weakly asymmetric limit of simple exclusion process with drift to the left, starting from step Bernoulli initial data with so that macroscopically one has…
Random graphs with a given degree sequence
Sourav Chatterjee, Persi Diaconis, Allan Sly
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild…
The missing log in large deviations for triangle counts
Sourav Chatterjee
This paper solves the problem of sharp large deviation estimates for the upper tail of the number of triangles in an Erdos-Renyi random graph, by establishing a logarithmic factor…