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Extrema of a multinomial assignment process

Part of: Special processes Combinatorial probability Graph theory

Published online by Cambridge University Press:  06 June 2023

Mikhail Lifshits Open the ORCID record for Mikhail Lifshits [Opens in a new window]  and
Gilles Mordant Open the ORCID record for Gilles Mordant [Opens in a new window]
Mikhail Lifshits*
Affiliation:
St. Petersburg State University
Gilles Mordant*
Affiliation:
Universität Göttingen
*
*Postal address: St. Petersburg State University. Russia, 199034, St. Petersburg, University Emb. 7/9. Email: mikhail@lifshits.org
**Postal address: Institut für Mathematische Stochastik, Universität Göttingen. Göttingen, Germany. Email: gilles.mordant@uni-goettingen.de
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Abstract

We study the asymptotic behaviour of the expectation of the maxima and minima of a random assignment process generated by a large matrix with multinomial entries. A variety of results is obtained for different sparsity regimes.

Keywords

Expected maximaminimamultinomial distributionrandom assignment process

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 05C70: Factorization, matching, partitioning, covering and packing 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 1 , March 2024 , pp. 198 - 213
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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