6 papers · 1 filter
Fluctuations for diameter and perimeter of convex hulls of multiple random walks
Wojciech Cygan, Tomislav Kralj, Nikola Sandrić +3
We study the diameter and perimeter of the convex hull generated by finitely many independent planar random walks whose increments have finite second moments. The large-time fluctu…
Perimeter length of the convex hull of Brownian motion in the hyperbolic plane
Chinmoy Bhattacharjee, Rik Versendaal, Andrew Wade
We relate the expected hyperbolic length of the perimeter of the convex hull of the trajectory of Brownian motion in the hyperbolic plane to an expectation of a certain exponential…
Central limit theorem for superdiffusive reflected Brownian motion
Aleksandar Mijatović, Isao Sauzedde, Andrew Wade
We study the second-order asymptotics around the superdiffusive strong law~\cite{MMW} of a multidimensional driftless diffusion with oblique reflection from the boundary in a gener…
Long-range one-dimensional internal diffusion-limited aggregation
Conrado da Costa, Debleena Thacker, Andrew Wade
We study internal diffusion limited aggregation on , where a cluster is grown incrementally by adding, for each random walk dispatched from the origin, the first site i…
Superdiffusive limits for stochastic kinetics driven by self-similar drifts
Miha Brešar, Conrado da Costa, Aleksandar Mijatović +1
We prove anomalous-diffusion scaling for a one-dimensional stochastic kinetic dynamics, in which the stochastic drift is driven by an exogenous self-similar noise, and also include…
Superdiffusive planar random walks with polynomial space-time drifts
Conrado da Costa, Mikhail Menshikov, Vadim Shcherbakov +1
We quantify superdiffusive transience for a two-dimensional random walk in which the vertical coordinate is a martingale and the horizontal coordinate has a positive drift that is…