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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

We achieve a detailed understanding of the n-sided planar PoissonVoronoi cell in the limit of large n. Let pn be the probability for a cell to have n sides. We construct the asymptotic expansion of log pn up to terms that vanish as n → ∞. We obtain the statistics of the lengths of the perimeter segments and of the angles between adjoining segments: to… (More)

- H. J. Hilhorst
- 2006

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

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

The kinetics of the q species pair annihilation reaction (Ai +Aj → ∅ 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. For d = 1 the system segregates into single species domains, yielding a different value of α for each q;… (More)

- H. J. Hilhorst
- 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)x2]1/(1−q). We show by explicit calculation that the probability… (More)

- H. J. Hilhorst
- 2008

I present a concise review of advances realized over the past three years on planar PoissonVoronoi tessellations. These encompass new analytic results, a new Monte Carlo method, and application to experimental data. PACS. PACS 02.50.-r Probability theory, stochastic processes, and statistics – PACS 45.70.Qj Pattern formation – PACS 87.18.-h Multicellular… (More)

- H. J. Hilhorst
- 2005

Let pn be the probability for a planar Poisson-Voronoi cell to have exactly n sides. We construct the asymptotic expansion of log pn 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 of… (More)

We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of shortrange infections that lead, at the critical point, to directed and isotropic percolation respectively, we consider long-range infections with a probability… (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
- 2008

By a new Monte Carlo algorithm we evaluate the sidedness probability pn 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 pn as n → ∞. Our pn values all have between four and six significant digits. Accurate n dependent… (More)