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- Riddhipratim Basu, Shirshendu Ganguly, Subhamoy Maitra, Goutam Paul
- J. Mathematical Cryptology
- 2008

Rotor walk is a deterministic analogue of random walk. We study its recurrence and transience properties on Z d for the initial configuration of all rotors aligned. If n particles in turn perform rotor walks starting from the origin, we show that the number that escape (i.e., never return to the origin) is of order n in dimensions d ≥ 3, and of order n/ log… (More)

- Sébastien Bubeck, Shirshendu Ganguly
- ArXiv
- 2015

We consider high dimensional Wishart matrices XX ⊤ where the entries of X ∈ R n×d are i.i.d. from a log-concave distribution. We prove an information theoretic phase transition: such matrices are close in total variation distance to the corresponding Gaussian ensemble if and only if d is much larger than n 3. Our proof is entropy-based, making use of the… (More)

- Laura Florescu, Shirshendu Ganguly, Lionel Levine, Yuval Peres
- SIAM J. Discrete Math.
- 2014

- Riddhipratim Basu, Arup Bose, Shirshendu Ganguly, Rajat Subhra Hazra
- 2012

J o u r n a l o f P r o b a b i l i t y Electron. Abstract We study the joint convergence of independent copies of several patterned matrices in the non-commutative probability setup. In particular, joint convergence holds for the well known Wigner, Toeplitz, Hankel, Reverse Circulant and Symmetric Circulant matrices. We also study some properties of the… (More)

We introduce a two-type internal DLA model which is an example of a non-unary abelian network. Starting with n " oil " and n " water " particles at the origin, the particles diffuse in Z according to the following rule: whenever some site x ∈ Z has at least 1 oil and at least 1 water particle present, it fires by sending 1 oil particle and 1 water particle… (More)

Let (G, ρ) be a stationary random graph, and use B G ρ (r) to denote the ball of radius r about ρ in G. Suppose that (G, ρ) has annealed polynomial growth, in the sense that E[|B G ρ (r)|] O(r k) for some k > 0 and every r 1. Then there is an infinite sequence of times {t n } at which the random walk {X t } on (G, ρ) is at most diffusive: Almost surely… (More)

- Bhaswar B. Bhattacharya, Sayantan Das, Shirshendu Ganguly
- Electr. J. Comb.
- 2014

In this paper we introduce the notion of minimum-weight edge-discriminators in hypergraphs, and study their various properties.

In 2006, the fourth author of this paper proposed a graph-theoretic model of interface dynamics called competitive erosion. Each vertex of the graph is occupied by a particle that can be either red or blue. New red and blue particles alternately get emitted from their respective bases and perform random walk. On encountering a particle of the opposite color… (More)