3 papers
math.PR2016
Kesten's incipient infinite cluster and quasi-multiplicativity of crossing probabilities
Deepan Basu, Artem Sapozhnikov
In this paper we consider Bernoulli percolation on an infinite connected bounded degrees graph . Assuming the uniqueness of the infinite open cluster and a quasi-multiplicativit…
math.PR2015
Crossing probabilities for critical Bernoulli percolation on slabs
Deepan Basu, Artem Sapozhnikov
We prove that in the critical Bernoulli percolation on two dimensional lattice slabs the probabilities of open left-right crossings of rectangles with any given aspect ratio are un…
math.CO2014
Almost Empty Monochromatic Triangles in Planar Point Sets
Deepan Basu, Kinjal Basu, Bhaswar B. Bhattacharya +1
For positive integers , let be the least integer such that any set of at least points in the plane, no three on a line and colored with col…