On the maximal displacement of near-critical branching random walks
On the maximal displacement of near-critical branching random walks
Abstract We consider a branching random walk on $$\mathbb {Z}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Z</mml:mi> </mml:math> started by n particles at the origin, where each particle disperses according to a mean-zero random walk with bounded support and reproduces with mean number of offspring $$1+\theta /n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>θ</mml:mi> <mml:mo>/</mml:mo> …