9 citations · 56 across the 26 of their papers we have counts for
19 papers · 1 filter
Occupation densities of Ensembles of Branching Random Walks
Si Tang, Steven P. Lalley
We study the limiting occupation density process for a large number of critical and driftless branching random walks. We show that the rescaled occupation densities of $\lfloor sN\…
Critical Branching Brownian Motion with Killing
Steven P. Lalley, Bowei Zheng
We obtain sharp asymptotic estimates for hitting probabilities of a critical branching Brownian motion in one dimension with killing at 0 We also obtain sharp asymptotic formulas f…
Contact Processes on Random Regular Graphs
Steven Lalley, Wei Su
We show that the contact process on a random -regular graph initiated by a single infected vertex obeys the "cutoff phenomenon" in its supercritical phase. In particular, we pro…
Maximal Displacement of Critical Branching Symmetric Stable Processes
Steven P. Lalley, Yuan Shao
We consider a critical continuous-time branching process (a Yule process) in which the individuals independently execute symmetric stable random motions on the real line starti…
Exchangeable Markov Processes on $[k]^{\zz{N}}$ with Cadlag Sample Paths
Harry Crane, Steven P. Lalley
Any exchangeable Markov processes on with cadlag sample paths projects to a Markov process on the simplex whose sample paths are cadlag and of locally bounded va…
Chernoff's distribution and differential equations of parabolic and Airy type
Piet Groeneboom, Steven Lalley, Nico Temme
We give a direct derivation of the distribution of the maximum and the location of the maximum of one-sided and two-sided Brownian motion with a negative parabolic drift. The argum…