Modul:   MAT591  Discrete mathematics

Dependency graphs and uniform bounds on cumulants

Vortrag von Prof. Dr. Valentin Féray

Datum: 14.03.17  Zeit: 11.15 - 12.15  Raum: Y27H46

Bounding cumulants is a standard way to prove asymptotic normality. Uniform bounds on cumulants enable to refine the asymptotic normality results, e.g. by giving an upper bound on the speed of convergence.
In this talk, we will see how to obtain uniform bounds on cumulants, when we have a dependency graph. This is based on the combinatorics of spanning trees. Two weighted variants will then be discussed.
Applications to pattern occurences in random permutations, subgraph counts in random graphs, magnetization/energy in Ising model and (multi)linear statistics of Markov chains will be given.