Contribution to the study of Markov loops.
type: Dataset
description: We are interested in Markov laces defined in the framework of the theory of Markov chains in continuous time on a discrete state space. This particular subject has been studied by Le Jan [LJ11] and Sznitman [Szn12]. In contrast to these references, we do not assume the reversibility of the chain and we are mostly interested in the case of countable state space. All the results are presented in terms of the generator of semigroup. In comparison with [LJ11], some demonstration has been detailed or improved.We also provide some results on the loop clusters (see [LJL12] in the reversible case). In particular, we study the example of discrete circle. We also study the spanning tree algorithm defined by Wilson in the non-symmetric case.In the last part, we consider the proportion of loops covering the whole space. Using the limit of the spectrums, we give a general expression for the limit of this ratio for a sequence of graphs. As an application, we give two examples in which a phase transition occurs.
identifier: NNT: 2013PA112069
issued: 2026-05-10T07:06:42.548945
language: fr
modified: 2026-05-10T07:06:42.548949
contact point: Organization
  fn: CCSD
keyword: amas-des-lacets
keyword: covering-loop
keyword: infoeu-reposemanticsdoctoralthesis
keyword: lacets-couvrant
keyword: lacets-markoviens
keyword: larbre-couvrant
keyword: loop-cluster
keyword: markovian-loops
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: spanning-tree
keyword: theses
landing page: https://theses.hal.science/tel-00846462

Contribution to the study of Markov loops.
type: Distribution
format: HTML
issued: 2026-05-10T07:06:42.570082
modified: 2026-05-10T07:06:42.537644
access URL: https://theses.hal.science/tel-00846462

test_moissonnage_selune
type: Agent