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SUMMARY:Almost upper directed Markov chains on trees
DTSTART:20250520T075000Z
DTEND:20250520T085000Z
DTSTAMP:20260610T152700Z
UID:indico-event-14251@indico.math.cnrs.fr
DESCRIPTION:Speakers: Luis Fredes (IMB)\n\nA transition matrix U on a tree
  T is said to be almost upper directed if the allowed steps are from a nod
 e to its parent or its descendants. In this talk\, as a warm-up\, I will s
 tart with the case where the tree is N and I will characterise the recurre
 nce\, positive recurrence\, and invariant distribution of these transition
  matrices. I will then present the theorems for general trees and a techni
 que that allows one to compute an invariant distribution at a given vertex
  without requiring knowledge of the full invariant measure. These results 
 encompass the case of birth and death processes (BDPs)\, which possess alm
 ost upper directed transition matrices. Their properties were studied in t
 he 1950s by Karlin and McGregor\, whose approach relies on deep connection
 s between the theory of BDPs\, the spectral properties of their transition
  matrices\, the moment problem\, and the theory of orthogonal polynomials.
  Our approach is mainly combinatorial and uses elementary algebraic method
 s. This talk is based on two joint works with J.-F. Marckert.\n\nhttps://i
 ndico.math.cnrs.fr/event/14251/
LOCATION:Amphi Schwartz
URL:https://indico.math.cnrs.fr/event/14251/
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