https://www.selleckchem.com/pr....oducts/CP-690550.htm
We investigate properties of the particle distribution near the tip of one-dimensional branching random walks at large times t, focusing on unusual realizations in which the rightmost lead particle is very far ahead of its expected position, but still within a distance smaller than the diffusion radius ∼sqrt[t]. Our approach consists in a study of the generating function G_Δλ)=∑_nλ^np_n(Δx) for the probabilities p_n(Δx) of observing n particles in an interval of given size Δx from the lead particle to its left, fixing the position o
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