Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Merlet, Glenn"'
Publikováno v:
Linear Algebra and its Applications 611 (2021) 279-309
Building on the weak CSR approach developed in a previous paper by Merlet, Nowak and Sergeev, we establish new bounds for the periodicity threshold of the powers of a tropical matrix. According to that approach, bounds on the ultimate periodicity thr
Externí odkaz:
http://arxiv.org/abs/2005.05390
Autor:
Izhakian, Zur, Merlet, Glenn
We introduce a faithful tropical linear representation of the Chinese monoid, and thus prove that this monoid admits all the semigroup identities satisfied by tropical triangular matrices.
Comment: 8 pages
Comment: 8 pages
Externí odkaz:
http://arxiv.org/abs/2001.05888
Autor:
Izhakian, Zur, Merlet, Glenn
We prove the conjecture that, for any $n$, the monoid of all $n \times n$ tropical matrices satisfies nontrivial semigroup identities. To this end, we prove that the factor rank of a large enough power of a tropical matrix does not exceed the tropica
Externí odkaz:
http://arxiv.org/abs/1806.11028
We study the transients of matrices in max-plus algebra. Our approach is based on the weak CSR expansion. Using this expansion, the transient can be expressed by $\max\{T_1,T_2\}$, where $T_1$ is the weak CSR threshold and $T_2$ is the time after whi
Externí odkaz:
http://arxiv.org/abs/1705.04104
Autor:
Izhakian, Zur1 (AUTHOR) zzur@g.ariel.ac.il, Merlet, Glenn2 (AUTHOR)
Publikováno v:
Semigroup Forum. Aug2023, Vol. 107 Issue 1, p144-157. 14p.
Weighted automata over the max-plus semiring S are closely related to finitely generated semigroups of matrices over S. In this paper, we use results in automata theory to study two quantities associated with sets of matrices: the joint spectral radi
Externí odkaz:
http://arxiv.org/abs/1612.02647
Publikováno v:
In Linear Algebra and Its Applications 15 February 2021 611:279-309
Autor:
Merlet, Glenn
On appelle suite récurrente stochastique (SRS) dirigée par une suite de matrices aléatoires une suite de variables aléatoires telles que le terme de rang n+1 est obtenu en multipliant celui de rang n par la enième matrice. Cette thèse porte sur
Externí odkaz:
http://tel.archives-ouvertes.fr/tel-00010813
http://tel.archives-ouvertes.fr/docs/00/04/86/95/PDF/tel-00010813.pdf
http://tel.archives-ouvertes.fr/docs/00/04/86/95/PDF/tel-00010813.pdf
Publikováno v:
Linear Algebra and its Applications 461 (2014) 163-199
This paper aims to unify and extend existing techniques for deriving upper bounds on the transient of max-plus matrix powers. To this aim, we introduce the concept of weak CSR expansions: A^t=CS^tR + B^t. We observe that most of the known bounds (imp
Externí odkaz:
http://arxiv.org/abs/1310.2475
We study sequences of optimal walks of a growing length, in weighted digraphs, or equivalently, sequences of entries of max-algebraic matrix powers with growing exponents. It is known that these sequences are eventually periodic when the digraphs are
Externí odkaz:
http://arxiv.org/abs/1307.3716