TY - JOUR
T1 - Optimal strong stationary times for random walks on the chambers of a hyperplane arrangement
AU - Nestoridi, Evita
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/8/1
Y1 - 2019/8/1
N2 - This paper studies Markov chains on the chambers of real hyperplane arrangements, a model that generalizes famous examples, such as the Tsetlin library and riffle shuffles. We discuss cutoff for the Tsetlin library for general weights, and we give an exact formula for the separation distance for the hyperplane arrangement walk. We introduce lower bounds, which allow for the first time to study cutoff for hyperplane arrangement walks under certain conditions. Using similar techniques, we also prove a uniform lower bound for the mixing time of Glauber dynamics on a monotone system.
AB - This paper studies Markov chains on the chambers of real hyperplane arrangements, a model that generalizes famous examples, such as the Tsetlin library and riffle shuffles. We discuss cutoff for the Tsetlin library for general weights, and we give an exact formula for the separation distance for the hyperplane arrangement walk. We introduce lower bounds, which allow for the first time to study cutoff for hyperplane arrangement walks under certain conditions. Using similar techniques, we also prove a uniform lower bound for the mixing time of Glauber dynamics on a monotone system.
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U2 - 10.1007/s00440-018-0872-7
DO - 10.1007/s00440-018-0872-7
M3 - Article
AN - SCOPUS:85053894240
SN - 0178-8051
VL - 174
SP - 929
EP - 943
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 3-4
ER -