This paper studies Markov chains on the symmetric group where the transition probabilities are given by the Ewens distribution with parameter . The eigenvalues are identified to be proportional to the content polynomials of partitions. We show that the mixing time is bounded above by a constant depending only on the parameter if is fixed. However, if it agrees with the number of permuted elements (), the sequence of chains has a total variation cutoff at .
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Keywords: Ewens distribution, mixing time, random walks on groups, YJM elements
CC-BY 4.0
@article{ALCO_2023__6_4_907_0,
author = {\"Ozdemir, Alperen},
title = {Random walks generated by the {Ewens} distribution on the symmetric group},
journal = {Algebraic Combinatorics},
pages = {907--927},
publisher = {The Combinatorics Consortium},
volume = {6},
number = {4},
year = {2023},
doi = {10.5802/alco.290},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.290/}
}
TY - JOUR AU - Özdemir, Alperen TI - Random walks generated by the Ewens distribution on the symmetric group JO - Algebraic Combinatorics PY - 2023 SP - 907 EP - 927 VL - 6 IS - 4 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.290/ DO - 10.5802/alco.290 LA - en ID - ALCO_2023__6_4_907_0 ER -
%0 Journal Article %A Özdemir, Alperen %T Random walks generated by the Ewens distribution on the symmetric group %J Algebraic Combinatorics %D 2023 %P 907-927 %V 6 %N 4 %I The Combinatorics Consortium %U https://alco.centre-mersenne.org/articles/10.5802/alco.290/ %R 10.5802/alco.290 %G en %F ALCO_2023__6_4_907_0
Özdemir, Alperen. Random walks generated by the Ewens distribution on the symmetric group. Algebraic Combinatorics, Volume 6 (2023) no. 4, pp. 907-927. doi : 10.5802/alco.290. https://alco.centre-mersenne.org/articles/10.5802/alco.290/
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