8 papers · 1 filter
Aging in a spin glass with logarithmic correlations
Aser Cortines, Oren Louidor, Heng Ma +1
We consider a continuous-time random walk on the discrete two dimensional box, driven by the discrete Gaussian Free Field (DGFF) acting as potential: When at a vertex, the walk wai…
Atypical Decay Rates for Atypical Heights in Random Recursive Trees
Xinxin Chen, Heng Ma
We establish the large deviation probabilities for the height of random recursive trees, revealing polynomial upper-tail decay and stretched-exponential lower-tail decay. Remarkabl…
Left Tail of the Derivative Martingale in a Gaussian BRW in the Entire Subcritical Regime
Xinxin Chen, Yichao Huang, Heng Ma
We establish a rather sharp two-sided estimate for the left tail probability of the derivative martingale limit in a binary Gaussian branching random walk throughout the entire sub…
Exponential moments of truncated branching random walk martingales
Heng Ma, Pascal Maillard
For a branching random walk that drifts to infinity, consider its Malthusian martingale, i.e.~the additive martingale with parameter being the smallest root of the characterist…
Branching brownian motion conditioned on large level sets
Xinxin Chen, Heng Ma
We study the precise large deviation probabilities for the sizes of intermediate level sets in branching Brownian motion (BBM). Our conclusions improve a result of Aïdekon, Hu and…
Multifractal spectrum of branching random walks on free groups
Shuwen Lai, Heng Ma, Longmin Wang
Consider a symmetric branching random walk on a free group in the transient regime , where is the mean offspring number and is the reciprocal of the…
Branching random walk conditioned on large martingale limit
Xinxin Chen, Loïc de Raphélis, Heng Ma
We consider a branching random walk in the non-boundary case where the additive martingale converges a.s. and in mean to some non-degenerate limit . We first establ…
Shotgun threshold for sparse Erdős-Rényi graphs
Jian Ding, Yiyang Jiang, Heng Ma
In the shotgun assembly problem for a graph, we are given the empirical profile for rooted neighborhoods of depth (up to isomorphism) for some and we wish to recover…