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08/15/2022
Speeding up random walk mixing by starting from a uniform vertex
The theory of rapid mixing random walks plays a fundamental role in the ...
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07/28/2022
Short Synchronizing Words for Random Automata
We prove that a uniformly random automaton with n states on a 2-letter a...
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04/16/2021
Rankings in directed configuration models with heavy tailed in-degrees
We consider the extremal values of the stationary distribution of sparse...
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10/14/2020
Minimum stationary values of sparse random directed graphs
We consider the stationary distribution of the simple random walk on the...
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06/07/2020
Two lower bounds for p-centered colorings
Given a graph G and an integer p, a coloring f : V(G) →ℕ is p-centered i...
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04/10/2020
The giant component of the directed configuration model revisited
We prove a law of large numbers for the order and size of the largest st...
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03/10/2020
The diameter of the directed configuration model
We show that the diameter of the directed configuration model with n ver...
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12/13/2018
The Glauber dynamics for edges colourings of trees
Let T be a tree on n vertices and with maximum degree Δ. We show that fo...
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10/30/2018
Improved Bounds for Randomly Sampling Colorings via Linear Programming
A well-known conjecture in computer science and statistical physics is t...
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04/11/2018