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In this paper we consider a simple virus infection spread model on a finite population of n agents connected by some neighborhood structure. Given a graph G on n vertices, we begin with some fixed number of initial infected vertices. At each discrete time step, an infected vertex tries to infect its neighbors with probability β ∈ (0, 1) independently of… (More)
For connectivity of random geometric graphs, where there is no density for underlying distribution of the vertices, we consider n i.i.d. Cantor distributed points on [0, 1]. We show that for this random geometric graph, the connectivity threshold R n , converges almost surely to a constant 1 − 2φ where 0 < φ < 1/2, which for standard Cantor distribution is… (More)
In this work we consider a simple SIR infection spread model on a finite population of n agents represented by a finite graph G. Starting with a fixed set of initial infected vertices the infection spreads in discrete time steps, where each infected vertex tries to infect its neighbors with a fixed probability β ∈ (0, 1), independently of others. It is… (More)
MSC: primary 60D05 05C80 secondary 60F15 60F25 60G70 Keywords: Cantor distribution Connectivity threshold Random geometric graph Singular distributions a b s t r a c t For the connectivity of random geometric graphs, where there is no density for the underlying distribution of the vertices, we consider n i.i.d. Cantor distributed points on [0, 1]. We show… (More)
To My Parents and My Sisters Acknowledgements First and above all, I praise God, the most merciful, for providing me the opportunity to step in one of the most beautiful areas in the world of science, Probability and Statistics. To be able to step strong in this way, I have also been supported by many people to whom I would like to express my sincerest… (More)
• Associate Professor: Working as a permanent faculty in the capacity of an associate professor at the Theoretical Statistics and Mathematics Division at the Indian Statistical Institute jointly with two of its centres at New Delhi and Calcutta, India: June 1, 2012-present.