Transport-entropy inequalities on locally acting groups of permutations

Paul-Marie Samson (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

Following Talagrand's concentration results for permutations picked uniformly at random from a symmetric group [Tal95], Luczak and McDiarmid have generalized it to more general groups G of permutations which act suitably 'locally'. Here we extend their results by setting transport-entropy inequalities on these permutations groups. Talagrand and Luczak-Mc-Diarmid concentration properties are consequences of these transport-entropy inequalities. We also consider transport-entropy inequalities on G for a larger class of measures. By projection, we derive transport-entropy inequalities for the uniform law on the slice of the discrete hypercube and more generally for the multinomial law. The transport-entropy inequalities settled in this paper are new examples, in discrete setting, of weak transport-entropy inequalities introduced in [GRST14].

Mots clés: Concentration of measure; Random permutation; Symmetric group; Slices of the discrete cube; Transport inequalities

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Paul-Marie Samson. Transport-entropy inequalities on locally acting groups of permutations. 2016. ⟨hal-01370491v1⟩