5 citations · 11 across the 9 of their papers we have counts for
11 papers
Böttcher-type potential for the secant map
Nicholas Freeman
We present a construction of a Böttcher-type holomorphic map for the potential of the secant method dynamical system near a root-type fixed point. The modulus of the Böttcher-type…
Tightness criteria for random compact sets of cadlag paths
Nic Freeman, Jan M. Swart
We give tightness criteria for random variables taking values in the space of all compact sets of cadlag real-valued paths, in terms of both the Skorohod J1 and M1 topologies. This…
Weaves, webs and flows
Nic Freeman, Jan Swart
We introduce weaves, which are random sets of non-crossing càdlàg paths that cover space-time . The Brownian web is one example of…
Skorokhod's topologies on path space
Nic Freeman, Jan M. Swart
Skorokhod's J1 and M1 topologies are standard tools in proving limit theorems for stochastic processes. Motivated by applications, we extend these topologies so that they are capab…
Extensive Condensation in a model of Preferential Attachment with Fitnesses
Nic Freeman, Jonathan Jordan
We introduce a new model of preferential attachment with fitness, and establish a time reversed duality between the model and a system of branching-coalescing particles. Using this…
Branching Brownian Motion, mean curvature flow and the motion of hybrid zones
Alison Etheridge, Nic Freeman, Sarah Penington
We provide a probabilistic proof of a well known connection between a special case of the Allen-Cahn equation and mean curvature flow. We then prove a corresponding result for scal…
Branching Brownian motion and Selection in the Spatial Lambda-Fleming-Viot Process
Alison Etheridge, Nic Freeman, Sarah Penington +1
We ask the question "when will natural selection on a gene in a spatially structured population cause a detectable trace in the patterns of genetic variation observed in the contem…
The Brownian Net and Selection in the Spatial Lambda-Fleming-Viot Process
Alison Etheridge, Nic Freeman, Daniel Straulino
We obtain the Brownian net of Sun and Swart (2008) as the scaling limit of the paths traced out by a system of continuous (one-dimensional) space and time branching and coalescing…
Cluster growth in the dynamical Erdős-Rényi process with forest fires
Edward Crane, Nic Freeman, Bálint Tóth
We investigate the growth of clusters within the forest fire model of Ráth and Tóth [22]. The model is a continuous-time Markov process, similar to the dynamical Erdős-Rényi random…
The number of non-singleton blocks in Lambda-coalescents with dust
Nic Freeman
In this article we state and prove a dichotomy, which is satisfied by the number of non-singleton blocks in Lambda-coalescents which have a dust component. The dichotomy is of a si…
The Segregated Lambda-coalescent
Nic Freeman
We construct an extension of the Lambda-coalescent to a spatial continuum and analyse its behaviour. Like the Lambda-coalescent, the individuals in our model can be separated into…