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- H J Hilhorst
- 2009

In this talk I first review at an elementary level a selection of central limit theorems, including some lesser known cases, for sums and maxima of uncorrelated and correlated random variables. I recall why several of them appear in physics. Next, I show that there is room for new versions of central limit theorems applicable to specific classes of… (More)

- H J Hilhorst
- 2008

I present a concise review of advances realized over the past three years on planar Poisson-Voronoi tessellations. These encompass new analytic results, a new Monte Carlo method, and application to experimental data.

- H J Hilhorst
- 2005

Let p n be the probability for a planar Poisson-Voronoi cell to have exactly n sides. We construct the asymptotic expansion of log p n up to terms that vanish as n → ∞. Along with it comes a nearly complete understanding of the structure of the large cell. We show that two independent biased random walks executed by the polar angle determine the trajectory… (More)

- H J Hilhorst, G Schehr
- 2008

The sum of N sufficiently strongly correlated random variables will not in general be Gaussian distributed in the limit N → ∞. We revisit examples of sums x that have recently been put forward as instances of variables obeying a q-Gaussian law, that is, one of type cst × [1 − (1 − q)x 2 ] 1/(1−q). We show by explicit calculation that the probability… (More)

- H J Hilhorst
- 2008

By a new Monte Carlo algorithm we evaluate the sidedness probability p n of a planar Poisson-Voronoi cell in the range 3 ≤ n ≤ 1600. The algorithm is developed on the basis of earlier theoretical work; it exploits, in particular, the known asymptotic behavior of p n as n → ∞. Our p n values all have between four and six significant digits. Accurate n… (More)

- H J Hilhorst
- 2006

In planar cellular systems m n denotes the average sidedness of a cell neighboring an n-sided cell. Aboav's empirical law states that nm n is linear in n. A downward curvature is nevertheless observed in the numerical nm n data of the Random Voronoi Froth. The exact large-n expansion of m n obtained in the present work, viz. m n = 4+3(π/n) 1 2 +. . .,… (More)

- F Van Wijland, S Caser, H J Hilhorst
- 2008

We study the support (i.e. the set of visited sites) of a t step random walk on a two-dimensional square lattice in the large t limit. A broad class of global properties M (t) of the support is considered, including, e.g., the number S(t) of its sites; the length of its boundary; the number of islands of unvisited sites that it encloses; the number of such… (More)

- H J Hilhorst
- 2009

We consider the d-dimensional Poisson-Voronoi tessellation and investigate the applicability of heuristic methods developed recently for two dimensions. Let p n (d) be the probability that a cell have n neighbors (be 'n-faced') and m n (d) the average facedness of a cell adjacent to an n-faced cell. We obtain the leading order terms of the asymptotic… (More)

- H J Hilhorst, P Calka
- 2008

We consider a family of random line tessellations of the Euclidean plane introduced in a much more formal context by Hug and Schneider [Geom. Funct. Anal. 17, 156 (2007)] and described by a parameter α ≥ 1. For α = 1 the zero-cell (that is, the cell containing the origin) coincides with the Crofton cell of a Poisson line tessellation, and for α = 2 it… (More)

- H J Hilhorst, O Deloubrì Ere, M J Washenberger, U C Täuber
- 2004

The kinetics of the q species pair annihilation reaction (A i + A j → ∅ for 1 ≤ i < j ≤ q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density decays as ρ(t) ∼ t −α. For d = 1 the system segregates into single species domains, yielding a different value of α for… (More)