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Cumulative processes in basketball games

I. Kopocińska, B. Kopociński (2006)

Applicationes Mathematicae

We assume that the current score of a basketball game can be modeled by a bivariate cumulative process based on some marked renewal process. The basic element of a game is a cycle, which is concluded whenever a team scores. This paper deals with the joint probability distribution function of this cumulative process, the process describing the host's advantage and its expected value. The practical usefulness of the model is demonstrated by analyzing the effect of small modifications of the model...

Cycle structure of percolation on high-dimensional tori

Remco van der Hofstad, Artëm Sapozhnikov (2014)

Annales de l'I.H.P. Probabilités et statistiques

In the past years, many properties of the largest connected components of critical percolation on the high-dimensional torus, such as their sizes and diameter, have been established. The order of magnitude of these quantities equals the one for percolation on the complete graph or Erdős–Rényi random graph, raising the question whether the scaling limits of the largest connected components, as identified by Aldous (1997), are also equal. In this paper, we investigate the cycle structureof the largest...

Cyclic random motions in ℝ d -space with n directions

Aimé Lachal (2006)

ESAIM: Probability and Statistics

We study the probability distribution of the location of a particle performing a cyclic random motion in ℝ d . The particle can take n possible directions with different velocities and the changes of direction occur at random times. The speed-vectors as well as the support of the distribution form a polyhedron (the first one having constant sides and the other expanding with time t). The distribution of the location of the particle is made up of two components: a singular component (corresponding...

Decay of covariances, uniqueness of ergodic component and scaling limit for a class of ∇ φ systems with non-convex potential

Codina Cotar, Jean-Dominique Deuschel (2012)

Annales de l'I.H.P. Probabilités et statistiques

We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. Using a technique which decouples the neighboring vertices into even and odd vertices, we show for a class of non-convex potentials: the uniqueness of ergodic component for ∇ φ -Gibbs measures, the decay of covariances, the scaling limit and the strict convexity of the surface tension.

Degenerate stochastic differential equations for catalytic branching networks

Sandra Kliem (2009)

Annales de l'I.H.P. Probabilités et statistiques

Uniqueness of the martingale problem corresponding to a degenerate SDE which models catalytic branching networks is proven. This work is an extension of the paper by Dawson and Perkins [Illinois J. Math.50 (2006) 323–383] to arbitrary catalytic branching networks. As part of the proof estimates on the corresponding semigroup are found in terms of weighted Hölder norms for arbitrary networks, which are proven to be equivalent to the semigroup norm for this generalized setting.

Determinantal transition kernels for some interacting particles on the line

A. B. Dieker, J. Warren (2008)

Annales de l'I.H.P. Probabilités et statistiques

We find the transition kernels for four markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin–McGregor-type kernel. The resulting kernels all inherit the determinantal structure from the Karlin–McGregor formula, and have a similar form to Schütz’s kernel for the totally asymmetric simple exclusion process.

Currently displaying 341 – 360 of 1452