Mathematics Colloquium

Wednesday, 11 October, 4 pm

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Venue: Ramanujan Hall

Host: Murali K. Srinivasan

Speaker: Subhajit Ghosh

Affiliation: Bar-Ilan University, Ramat-Gan, Israel

TITLE: Aldous-type spectral gap results for the complete monomial group

ABSTRACT: Let G be a finite group. We consider a connected graph such that the edges and vertices are equipped with independent Poisson clocks  (alarm clocks that ring at time distributed as the exponential distribution).  Also, there are lamps with configurations indexed by the elements of G and lamplighters at the vertices of the graph.  The lamplighters at a pair of neighboring vertices exchange their position whenever the associated edge rings.  The lamplighter at a vertex updates the lamp configuration whenever the vertex rings.  The process can be viewed as a continuous-time random walk on the complete monomial group G wreath S(n) (symmetric group).   If the configuration of a lamp is x, then it changes to g.x with a non-negative rate alpha(g).  We assume that the rates are symmetric, and the elements g in G with positive alpha(g) generate G.  We show that the spectral gap of the process is the same as that of the continuous-time lamplighter random walk (i.e., the process with a single lamplighter) on the graph.  This is an analog of the Aldous' spectral gap conjecture for the complete monomial group of degree n over G.

Statistics seminar

Wednesday 11th Oct, 5-6 pm

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Venue: Ramanujan Hall

Host: Siuli Mokhopadhyay

Speaker: Prof. Manisha Pal

Affiliation: St. Xavier's University, Kolkata

Title: EXACT INFERENCE IN A MULTINOMIAL DISTRIBUTION

Abstract: Sequential sampling plans for unbiased estimation of the Bernoulli parameter 'p' have been studied for almost 70 years. Thereafter, there have been some studies for unbiasedly estimating functions of p. An extension of the idea to parametric function estimation in a trinomial distribution has been considered briefly. In this paper we address the problem of finding unbiased estimators of the parameters p and q in a tetranomial distribution, where the cell probabilities are p2, q2, r2, and 2(pq + pr + qr), satisfying p, q, r > 0, p + q + r = 1. Some illustrative examples have been cited to demonstrate the underlying concepts and the computational procedure.