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math.PR2004★ 4 cited
The spectrum of a random geometric graph is concentrated
Sanatan Rai
Consider points distributed uniformly in . Form a graph by connecting two points if their mutual distance is no greater than . This gives a random geometric grap…
math.PR2003★ 61 cited
Monotone properties of random geometric graphs have sharp thresholds
Ashish Goel, Sanatan Rai, Bhaskar Krishnamachari
Random geometric graphs result from taking uniformly distributed points in the unit cube, , and connecting two points if their Euclidean distance is at most , for s…
math.PR2003
A non constructive proof of the existence of a maximal irreducibility measure
Sanatan Rai
We deduce the existence of a maximal irreducibility measure for a Markov chain from Zorn's lemma.