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The triangle and the open triangle

Gady Kozma (2011)

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

We show that for percolation on any transitive graph, the triangle condition implies the open triangle condition.

The unscaled paths of branching brownian motion

Simon C. Harris, Matthew I. Roberts (2012)

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

For a set A ⊂ C[0, ∞), we give new results on the growth of the number of particles in a branching Brownian motion whose paths fall within A. We show that it is possible to work without rescaling the paths. We give large deviations probabilities as well as a more sophisticated proof of a result on growth in the number of particles along certain sets of paths. Our results reveal that the number of particles can oscillate dramatically. We also obtain new results on the number of particles near the...

The weak convergence of regenerative processes using some excursion path decompositions

Amaury Lambert, Florian Simatos (2014)

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

We consider regenerative processes with values in some general Polish space. We define their ε -big excursions as excursions e such that ϕ ( e ) g t ; ε , where ϕ is some given functional on the space of excursions which can be thought of as, e.g., the length or the height of e . We establish a general condition that guarantees the convergence of a sequence of regenerative processes involving the convergence of ε -big excursions and of their endpoints, for all ε in a set whose closure contains 0 . Finally, we provide...

Currently displaying 101 – 120 of 145