arXiv subjects
Publications and source records attributed to Shubhabrata Das.
In this paper we prove that: Any graph product of finitely many groups, all of them satisfying weak Haagerup property with $Λ_{WH}=1$, also satisfies weak Haagerup property and as a corollary of this result we obtain that the free product of weakly Haagerup groups with $Λ_{WH}=1$, again has weak Haagerup property with $Λ_{WH}=1$.
In this paper, we prove that any graph product of finitely many groups, all satisfying the Haagerup property (or Gromov's a-T-menability) also satisfies Haagerup property.
Predicting the winner of an election is of importance to multiple stakeholders. To formulate the problem, we consider an independent sequence of categorical data with a finite number of possible outcomes in each. The data is assumed to be observed in batches, each of which is based on a large number of such trials and can be modeled via multinomial distributions. We postulate that the multinomial probabilities of the categories vary randomly depending on batches. The challenge is to predict accurately on cumulative data based on data up to a few batches as early as possible. On the theoretical front, we first derive sufficient conditions of asymptotic normality of the estimates of the multinomial cell probabilities and present corresponding suitable transformations. Then, in a Bayesian framework, we consider hierarchical priors using multivariate normal and inverse Wishart distributions and establish the posterior convergence. The desired inference is arrived at using these results and ensuing Gibbs sampling. The methodology is demonstrated with election data from two different settings -- one from India and the other from the United States of America. Additional insights of the effectiveness of the proposed methodology are attained through a simulation study.
The success of a football team depends on various individual skills and performances of the selected players as well as how cohesively they perform. We propose a two-stage process for selecting optimal playing eleven of a football team from its pool of available players. In the first stage a LASSO-induced modified multinomial logistic regression model is derived to analyse the probabilities of the three possible outcomes. The model considers strengths of the players in the team as well as those of the opponent, home advantage, and also the effects of individual players and player combinations beyond the recorded performances of these players. In the second stage, a GRASP-type meta-heuristic is implemented for the team selection which maximises its probability of winning. The work is illustrated with English Premier League data from 2008/09 to 2015/16. The application demonstrates that the model in the first stage furnishes valuable insights about the deciding factors for different teams whereas the optimisation steps can be effectively used to determine the best possible starting lineup under various circumstances. We propose a measure of efficiency in team selection by the team management and analyse the performance of the teams on this front.
We introduce the notion of controlled Floyd separation between geodesic rays starting at the identity in a finitely generated group G. Two such geodesic rays are said to be Floyd separated with respect to quasigeodesics if the (Floyd) length of c-quasigeodesics (for fixed but arbitrary c) joining points on the geodesic rays is asymptotically bounded away from zero. This is always satisfied by Morse geodesics. The main purpose of this paper is to furnish an example of a finitely generated group $G$ such that 1) all finitely presented subgroups of G are hyperbolic, 2) G has an uncountable family of geodesic rays that are Floyd separated with respect to quasigeodesics, 3) G is not hyperbolic relative to any collection of proper subgroups. 4) G is a direct limit of hyperbolic CAT(0) cubulated groups. 5) G has trivial Floyd boundary in the usual sense. On the way towards constructing $G$, we construct a malnormal infinitely generated (and hence non-quasiconvex) subgroup of a free group, giving negative evidence towards a question of Swarup and Gitik.
We prove the existence of Cannon-Thurston maps for Kleinian groups corresponding to pared manifolds whose boundary is incompressible away from cusps. We also describe the structure of these maps in terms of ending laminations.
One possible way of risk management for an insurance company is to develop an early and appropriate alarm system before the possible ruin. The ruin is defined through the status of the aggregate risk process, which in turn is determined by premium accumulation as well as claim settlement outgo for the insurance company. The main purpose of this work is to design an effective alarm system, i.e. to define alarm times and to recommend augmentation of capital of suitable magnitude at those points to prevent or reduce the chance of ruin. To draw a fair measure of effectiveness of alarm system, comparison is drawn between an alarm system, with capital being added at the sound of every alarm, and the corresponding system without any alarm, but an equivalently higher initial capital. Analytical results are obtained in general setup and this is backed up by simulated performances with various types of loss severity distributions. This provides a strategy for suitably spreading out the capital and yet addressing survivability concerns at satisfactory level.
In earlier work, we had shown that Cannon-Thurston maps exist for Kleinian punctured surface groups without accidental parabolics. In this note we prove that pre-images of points are precisely end-points of leaves of the ending lamination whenever the Cannon-Thurston map is not one-to-one. This extends earlier work done for closed surface groups.