Évènements

Imagine a collection of randomly distributed points in space, and build a graph on it according to some rules. We now take the sum of all edge lengths and want to know if this sum verifies a central limit theorem. In our context, the random collection of points is given by a Poisson measure and the sum of edge lengths is an example of a Poisson functional. In this talk, using the so-called Malliavin-Stein method, we show a result which allows us to derive central limit theorems, as well as speeds of convergence, for functionals of general Poisson measures, under minimal moment assumptions. Our main application is the closure of a conjecture about a convergence result of the Online Nearest Neighbour Graph.

Lagrange spectrum is related to the rational approximations of badly approximable numbers. The discrete part of the spectrum is denoted in terms of Christoffel words. Multiplicative analogy of Lagrange spectrum was recently investigated, which is defined by rational approximations of geometric sequences and more general linear recurrence. Dubickas essentially found the relation of the discrete part of the multiplicative Lagrange spectrum and the limit sup words on the shift spaces with alternate order. Liao and Steiner found that such words are also related to the negative beta expansions. On this talk, we shall investigate limit sup words on more general ordered shift spaces. Such words are related to generalized beta expansion.

This is a joint work with Wolfgang Steiner.

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