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Tuesday, September 9, 2014 - 16:45 to 17:45
Dr. Ghurumuruhan Ganesan
EPFL, Lausanne
Infection Spread and Stability in Random Graphs
Abstract: In the first part of the talk, we study infection spread in random geometric graphs where $n$ nodes are distributed uniformly in the unit square $W$ centred at the origin and two nodes are joined by an edge if the Euclidean distance between them is less than $r_n$. Assuming edge passage times are exponentially distributed with unit mean, we obtain upper and lower bounds for speed of infection spread in the sub-connectivity regime, $nr^2_n \to \infty$. In the second part of the talk, we discuss convergence rate of sums of locally determinable functionals of Poisson processes. Denoting the Poisson process as $\mathcal{N}$ , the functional as $f$ and Lebesgue measure as $l(.)$, we establish corresponding bounds for $$\frac{1}{l(nW)}\sum_{x\in nW \cap \mathcal{N}} f(x)$$ in terms of the decay rate of the radius of determinability.

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