| Title:
|
A determinant formula from random walks (English) |
| Author:
|
Randriamaro, Hery |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
59 |
| Issue:
|
5 |
| Year:
|
2023 |
| Pages:
|
421-431 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
random walk |
| Keyword:
|
stochastic matrix |
| Keyword:
|
distance function |
| Keyword:
|
determinant |
| MSC:
|
05B20 |
| MSC:
|
15A15 |
| MSC:
|
60C05 |
| MSC:
|
60J10 |
| idZBL:
|
Zbl 07790557 |
| idMR:
|
MR4641956 |
| DOI:
|
10.5817/AM2023-5-421 |
| . |
| Date available:
|
2023-08-15T13:40:40Z |
| Last updated:
|
2024-02-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151798 |
| . |
| Reference:
|
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| Reference:
|
[2] Horn, R., Johnson, Ch.: Matrix analysis.Cambridge University Press, 2012. MR 2978290 |
| Reference:
|
[3] Krattenthaler, Ch.: Advanced determinant calculus.The Andrews Festschrift: Seventeen Papers on Classical Number Theory and Combinatorics, Springer, 2001, pp. 349–426. MR 1701596 |
| Reference:
|
[4] Krattenthaler, Ch.: Advanced determinant calculus: a complement.Linear Algebra Appl. 411 (2005), 68–166. Zbl 1079.05008, MR 2178686 |
| Reference:
|
[5] Randriamaro, H.: The Varchenko determinant for apartments.Results Math. 75 (2020), no. 3, 1–17. MR 4105756, 10.1007/s00025-020-01226-z |
| Reference:
|
[6] Shattuck, M.: Parity theorems for statistics on permutations and Catalan words.Integers 5 (2005), no. 1, Paper–A07. MR 2139163 |
| . |
