Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 18-43
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A. M. Borodin. Law of large numbers and central limit theorem for Jordan normal form of large triangular matrices over a finite field. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 18-43. http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a1/
@article{ZNSL_1997_240_a1,
author = {A. M. Borodin},
title = {Law of large numbers and central limit theorem for {Jordan} normal form of large triangular matrices over a finite field},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {18--43},
year = {1997},
volume = {240},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a1/}
}
TY - JOUR
AU - A. M. Borodin
TI - Law of large numbers and central limit theorem for Jordan normal form of large triangular matrices over a finite field
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1997
SP - 18
EP - 43
VL - 240
UR - http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a1/
LA - ru
ID - ZNSL_1997_240_a1
ER -
%0 Journal Article
%A A. M. Borodin
%T Law of large numbers and central limit theorem for Jordan normal form of large triangular matrices over a finite field
%J Zapiski Nauchnykh Seminarov POMI
%D 1997
%P 18-43
%V 240
%U http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a1/
%G ru
%F ZNSL_1997_240_a1
We prove that for a typical stricly uppertriangular matrix of order $n$ over a finite field with $q$ elements the sequence of orders of Jordan blocks, divided by $n$, converges to the geometric progression $\{(q-1)q^{-k},\,k=1, 2,\dots\}$, $n\to\infty$. We also show that the distribution of orders for a finite number of Jordan blocks is asymptotically normal. The corresponding covariance matrix is calculated.
