Random networks with sublinear preferential attachment: degree evolutions.
Small scale limit theorems for the intersection local times of Brownian motion.
Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst.
The average density of super-brownian motion
Upper tail asymptotics for the intersection local times of random walks in high dimensions
In high dimensions two independent simple random walks have only a finite number of intersections. I describe the main result obtained in a joint paper with Xia Chen in which we determine the exact upper tail behaviour of the intersection local time.
Tangent Measure Distributions of Hyperbolic Cantor Sets.
Ageing in the parabolic Anderson model
The parabolic Anderson model is the Cauchy problem for the heat equation with a random potential. We consider this model in a setting which is continuous in time and discrete in space, and focus on time-constant, independent and identically distributed potentials with polynomial tails at infinity. We are concerned with the long-term temporal dynamics of this system. Our main result is that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly over time,...
Large deviations of Markov chains indexed by random trees
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