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PARTIAL SHUFFLES BY LAZY SWAPS.
- Source :
-
SIAM Journal on Discrete Mathematics . 2023, Vol. 37 Issue 4, p2544-2557. 14p. - Publication Year :
- 2023
-
Abstract
- How many random transpositions (meaning that we swap given pairs of elements with given probabilities independently) are needed to ensure that each element of [n] is uniformly distributed--in the sense that the probability that i is mapped to j is 1/n for all i and j And what if we insist that each pair is uniformly distributed In this paper we show that the minimum for the first problem is about 1 2nlog2 n, with this being exact when n is a power of 2. For the second problem, we show that, rather surprisingly, the answer is not quadratic: O(nlog2 n) random transpositions suffice. We also show that if we ask only that the pair (1, 2) is uniformly distributed, then the answer is 2n 3. This proves a conjecture of Groenland, Johnston, Radcliffe, and Scott. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08954801
- Volume :
- 37
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 175427640
- Full Text :
- https://doi.org/10.1137/22M1530677