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Hausdorff and packing dimensions of the images of random fields
Hausdorff packing dimensions the images of random fields
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2010/11/24
Let $X=\{X(t),t\in\mathbb{R}^N\}$ be a random field with values in $\mathbb{R}^d$. For any finite Borel measure $\mu$ and analytic set $E\subset\mathbb{R}^N$, the Hausdorff and packing dimensions of t...
Epidemics on random intersection graphs
Epidemics random intersection graphs
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2010/11/23
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Removed) epidemic on a network of individuals described by a random intersection graph. The nu...
Homogenization of the G-equation with incompressible random drift in two dimensions
the G-equation incompressible dimensions
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2010/11/8
We study the homogenization limit of solutions to the G-equation with random drift. This Hamilton-Jacobi equation is a model for flame propagation in a turbulent fluid in the regime of thin flames. F...
The threshold-two contact process on a random r-regular graph has a first order phase transition
The threshold-two contact process r-regular graph phase transition
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2010/11/12
We consider the discrete time threshold-two contact process on a random $r$-regular graph on $n$ vertices. In this process, a vertex with at least two occupied neighbors at time $t$ will be occupied ...
From random sets to continuous tensor products: answers to three questions of W. Arveson
continuous tensor products W. Arveson
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2010/10/29
The set of zeros of a Brownian motion gives rise to a product system in the sense of William Arveson (that is, a continuous tensor product system of Hilbert spaces). Replacing the Brownian motion with...