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Quenched law of large numbers for branching brownian motion in a random medium

János Engländer (2008)

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

We study a spatial branching model, where the underlying motion is d-dimensional (d≥1) brownian motion and the branching rate is affected by a random collection of reproduction suppressing sets dubbed mild obstacles. The main result of this paper is the quenched law of large numbers for the population for all d≥1. We also show that the branching brownian motion with mild obstacles spreads less quickly than ordinary branching brownian motion by giving an upper estimate on its speed. When the underlying...

Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy

Tadeusz Nadzieja, Andrzej Raczyński (2000)

Applicationes Mathematicae

We consider the following problem: Δ Φ = ± M ο v e r ∫ Ω e - Φ / Θ e - Φ / Θ , E = M Θ ∓ 1 ο v e r 2 ∫ Ω | ∇ Φ | 2 , Φ | ∂ Ω = 0 , where Φ: Ω ⊂ ℝ n → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.

Random spatial growth with paralyzing obstacles

J. van den Berg, Y. Peres, V. Sidoravicius, M. E. Vares (2008)

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

We study models of spatial growth processes where initially there are sources of growth (indicated by the colour green) and sources of a growth-stopping (paralyzing) substance (indicated by red). The green sources expand and may merge with others (there is no ‘inter-green’ competition). The red substance remains passive as long as it is isolated. However, when a green cluster comes in touch with the red substance, it is immediately invaded by the latter, stops growing and starts to act as a red...

Random walks on finite rank solvable groups

Ch. Pittet, Laurent Saloff-Coste (2003)

Journal of the European Mathematical Society

We establish the lower bound p 2 t ( e , e ) ≿ exp ( − t 1 / 3 ) , for the large times asymptotic behaviours of the probabilities p 2 t ( e , e ) of return to the origin at even times 2 t , for random walks associated with finite symmetric generating sets of solvable groups of finite Prüfer rank. (A group has finite Prüfer rank if there is an integer r , such that any of its finitely generated subgroup admits a generating set of cardinality less or equal to r .)

Resonant delocalization for random Schrödinger operators on tree graphs

Michael Aizenman, Simone Warzel (2013)

Journal of the European Mathematical Society

We analyse the spectral phase diagram of Schrödinger operators T + λ V on regular tree graphs, with T the graph adjacency operator and V a random potential given by i i d random variables. The main result is a criterion for the emergence of absolutely continuous ( a c ) spectrum due to fluctuation-enabled resonances between distant sites. Using it we prove that for unbounded random potentials a c spectrum appears at arbitrarily weak disorder ( λ ≪ 1 ) in an energy regime which extends beyond the spectrum of ∼ T . Incorporating...

Currently displaying 401 – 420 of 591