# Law of Large Numbers for infinite random matrices over a finite field

@article{Bufetov2014LawOL,
title={Law of Large Numbers for infinite random matrices over a finite field},
author={Alexey Bufetov and Leonid Petrov},
journal={Selecta Mathematica},
year={2014},
volume={21},
pages={1271-1338}
}
• Published 7 February 2014
• Mathematics
• Selecta Mathematica
Asymptotic representation theory of general linear groups $$\hbox {GL}(n,F_\mathfrak {q})$$GL(n,Fq) over a finite field leads to studying probability measures $$\rho$$ρ on the group $$\mathbb {U}$$U of all infinite uni-uppertriangular matrices over $$F_\mathfrak {q}$$Fq, with the condition that $$\rho$$ρ is invariant under conjugations by arbitrary infinite matrices. Such probability measures form an infinite-dimensional simplex, and the description of its extreme points (in other words…
Neretin constructed an analogue of the Hua measures on the infinite $p$-adic matrices $Mat\left(\mathbb{N},\mathbb{Q}_p\right)$. Bufetov and Qiu classified the ergodic measures on
We show that singular numbers (also known as invariant factors or Smith normal forms) of products and corners of random matrices over $\mathbb{Q}_p$ are governed by the Hall-Littlewood polynomials,
• Mathematics
International Mathematics Research Notices
• 2020
We present a probabilistic generalization of the Robinson–Schensted correspondence in which a permutation maps to several different pairs of standard Young tableaux with nonzero probability. The
• Mathematics
• 2014
We show that the order on probability measures, inherited from the dominance order on the Young diagrams, is preserved under natural maps reducing the number of boxes in a diagram by $1$. As a
• Mathematics
• 2015
We introduce and study q-randomized Robinson-Schensted-Knuth (RSK) correspondences which interpolate between the classical (q=0) and geometric (q->1) RSK correspondences (the latter ones are
• Mathematics
Forum of Mathematics, Pi
• 2020
Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions. These measures are a useful tool to uncover the
We prove the classification of homomorphisms from the algebra of symmetric functions to $\mathbb{R}$ with non-negative values on Macdonald symmetric functions $P_{\lambda}$, that was conjectured by
Integrable probability has emerged as an active area of research at the interface of probability/mathematical physics/statistical mechanics on the one hand, and representation theory/integrable
• Mathematics
Forum of Mathematics, Sigma
• 2019
Employing bijectivization of summation identities, we introduce local stochastic moves based on the Yang–Baxter equation for $U_{q}(\widehat{\mathfrak{sl}_{2}})$ . Combining these moves leads to a

## References

SHOWING 1-10 OF 78 REFERENCES

• Mathematics
• 1996
Let $H$ be the space of all Hermitian matrices of infinite order and $U(\infty)$ be the inductive limit of the chain $U(1)\subset U(2)\subset...$ of compact unitary groups. The group $U(\infty)$
• Mathematics
• 2014
Macdonald processes are probability measures on sequences of partitions defined in terms of nonnegative specializations of the Macdonald symmetric functions and two Macdonald parameters $$q,t \in We present a unified approach to various examples of Markov dynamics on partitions studied by Borodin, Olshanski, Fulman, and the author. Our technique generalizes Kerov’s operators which first • Mathematics Proceedings of the National Academy of Sciences of the United States of America • 1951 A real matrix, finite or infinite, is called totally positive if and only if all its minors, of all orders = 1, 2,..., are non-negative. An infinite sequence$$ {a_0},{a_1},{a_2}, \ldots ,\quad
Abstract The conjugacy classes of the finite general linear and unitary groups are used to define probability measures on the set of all partitions of all natural numbers. Probabilistic algorithms
The conjugacy classes of the nite general linear and unitary groups are used to de ne probability measures on the set of all partitions of all natural numbers. Probabilistic algorithms for growing
Abstract. Let g be a random element of a finite classical group G, and let λz-1(g) denote the partition corresponding to the polynomial z - 1 in the rational canonical form of g. As the rank of G
• Mathematics
• 2011
Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains