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Cutoff for conjugacy-invariant random wa...

Berestycki, Nathanae...

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Cutoff for conjugacy-invariant random walks on the permutation group by Berestycki, Nathanael ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	06-09-2023
Summary	We prove a conjecture raised by the work of Diaconis and Shahshahani (1981) about the mixing time of random walks on the permutation group induced by a given conjugacy class. To do this we exploit a connection with coalescence and fragmentation processes and control the Kantorovitch distance by using a variant of a coupling due to Oded Schramm. Recasting our proof in the language of Ricci curvature, our proof establishes the occurrence of a phase transition, which takes the following form in the case of random transpositions: at time $cn/2$, the curvature is asymptotically zero for $c\le 1$ and is strictly positive for $c>1$.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1410.4800

Citation

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AMA 11th EditionReferences

Berestycki, Nathanael. Cutoff for conjugacy-invariant random walks on the permutation group. Australian National University. September 06, 2023. Accessed September 20, 2024. https://online.provdatabase.com/cite/23721

APA 7th EditionReferences

Berestycki, Nathanael. (2023). Cutoff for conjugacy-invariant random walks on the permutation group. Australian National University. https://online.provdatabase.com/cite/23721

Chicago 17th EditionReferences

Berestycki, Nathanael. Cutoff for conjugacy-invariant random walks on the permutation group. Australian National University. 2023. https://online.provdatabase.com/cite/23721

HarvardReferences

Berestycki, Nathanael. (2023). Cutoff for conjugacy-invariant random walks on the permutation group. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/23721. (Accessed 20 September 2024).

Harvard AustraliaReferences

Berestycki, Nathanael, 2023, Cutoff for conjugacy-invariant random walks on the permutation group, Australian National University, viewed 20 September 2024, <https://online.provdatabase.com/cite/23721>

MLA 9th EditionWorks Cited

Berestycki, Nathanael. Cutoff for conjugacy-invariant random walks on the permutation group. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/23721.

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