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)
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)
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)
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)
The prevalent technique for DNA sequencing consists of two main steps: shotgun sequencing, where many randomly located fragments, called reads, are extracted from the overall sequence, followed by an assembly algorithm that aims to reconstruct the original sequence. There are many different technologies that generate the reads: widely-used second-generation… (More)
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)
Consider " Frozen Random Walk " on Z: n particles start at the origin. At any discrete time, the leftmost and rightmost n 4 particles are " frozen " and do not move. The rest of the particles in the " bulk " independently jump to the left and right uniformly. The goal of this note is to understand the limit of this process under scaling of mass and time. To… (More)
In this paper we introduce the notion of minimum-weight edge-discriminators in hypergraphs, and study their various properties.