In angle-dependent 2D branching Brownian motion with b(θ) = 1 - β|θ|^α + O(θ²) near θ=0 for α ∈ (2/3,2), the maximum M_t satisfies that M_t - m(t) is tight with m(t) = √2 t - (ϑ₁/√2) t^{(2-α)/(2+α)} - c log t, where ϑ₁ comes from the first eigenvalue of an associated operator.
On the growth of the extremal and cluster level sets in branching brownian motion.arXiv preprint arXiv:2405.17634, 2024
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.PR 2verdicts
UNVERDICTED 2representative citing papers
Establishes O(1)-tightness for first passage times of d-dimensional branching random walks as distance x tends to infinity, resolving a prior conjecture.
citing papers explorer
-
Polynomial slowdown in an angle-dependent 2d branching Brownian motion
In angle-dependent 2D branching Brownian motion with b(θ) = 1 - β|θ|^α + O(θ²) near θ=0 for α ∈ (2/3,2), the maximum M_t satisfies that M_t - m(t) is tight with m(t) = √2 t - (ϑ₁/√2) t^{(2-α)/(2+α)} - c log t, where ϑ₁ comes from the first eigenvalue of an associated operator.
-
Tightness Analysis of First Passage Times of $d$-Dimensional Branching Random Walk
Establishes O(1)-tightness for first passage times of d-dimensional branching random walks as distance x tends to infinity, resolving a prior conjecture.