Journal article
Cut-off phenomenon for the ax+b Markov chain over a finite field
- Abstract:
- We study the Markov chain xn+1= axn+ bn on a finite field Fp, where a∈Fp× is fixed and bn are independent and identically distributed random variables in Fp. Conditionally on the Riemann hypothesis for all Dedekind zeta functions, we show that the chain exhibits a cut-off phenomenon for most primes p and most values of a∈Fp×. We also obtain weaker, but unconditional, upper bounds for the mixing time.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Accepted manuscript, pdf, 509.0KB, Terms of use)
-
- Publisher copy:
- 10.1007/s00440-022-01161-w
Authors
- Publisher:
- Springer
- Journal:
- Probability Theory and Related Fields More from this journal
- Volume:
- 184
- Issue:
- 1
- Pages:
- 85-113
- Publication date:
- 2022-09-02
- Acceptance date:
- 2022-08-13
- DOI:
- EISSN:
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1432-2064
- ISSN:
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0178-8051
- Language:
-
English
- Keywords:
- Pubs id:
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1278557
- Local pid:
-
pubs:1278557
- Deposit date:
-
2024-10-25
Terms of use
- Copyright holder:
- Breuillard et al.
- Copyright date:
- 2022
- Rights statement:
- Copyright © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Springer at https://dx.doi.org/10.1007/s00440-022-01161-w
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