A determinant formula from random walks
Archivum Mathematicum (2023)
- Volume: 059, Issue: 5, page 421-431
- ISSN: 0044-8753
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topRandriamaro, Hery. "A determinant formula from random walks." Archivum Mathematicum 059.5 (2023): 421-431. <http://eudml.org/doc/299135>.
@article{Randriamaro2023,
abstract = {One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute the determinant of a large class of matrices. Two examples involving digraphs and hyperplane arrangements are provided.},
author = {Randriamaro, Hery},
journal = {Archivum Mathematicum},
keywords = {random walk; stochastic matrix; distance function; determinant},
language = {eng},
number = {5},
pages = {421-431},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A determinant formula from random walks},
url = {http://eudml.org/doc/299135},
volume = {059},
year = {2023},
}
TY - JOUR
AU - Randriamaro, Hery
TI - A determinant formula from random walks
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 5
SP - 421
EP - 431
AB - One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute the determinant of a large class of matrices. Two examples involving digraphs and hyperplane arrangements are provided.
LA - eng
KW - random walk; stochastic matrix; distance function; determinant
UR - http://eudml.org/doc/299135
ER -
References
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- Krattenthaler, Ch., Advanced determinant calculus, The Andrews Festschrift: Seventeen Papers on Classical Number Theory and Combinatorics, Springer, 2001, pp. 349–426. (2001) MR1701596
- Krattenthaler, Ch., Advanced determinant calculus: a complement, Linear Algebra Appl. 411 (2005), 68–166. (2005) Zbl1079.05008MR2178686
- Randriamaro, H., 10.1007/s00025-020-01226-z, Results Math. 75 (2020), no. 3, 1–17. (2020) MR4105756DOI10.1007/s00025-020-01226-z
- Shattuck, M., Parity theorems for statistics on permutations and Catalan words, Integers 5 (2005), no. 1, Paper–A07. (2005) MR2139163
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