Comment on ''Understanding the Area Proposal for Extremal Black Hole Entropy''

A. Ghosh and P. Mitra made the proposal how to explain the area law for the entropy of extreme black holes in some model calculations. I argue that their approach implicitly operates with strongly singular geometries and says nothing about the contribution of regular metrics of extreme black holes into the partition function.Comment: 5 pages, ReVTeX, no figures. Expanded from the journal version to include response to Ghosh and Mitra Reply

Exact dimer ground states for a continuous family of quantum spin chains

Using the matrix product formalism, we define a multi-parameter family of spin models on one dimensional chains, with nearest and next-nearest neighbor anti-ferromagnetic interaction for which exact analytical expressions can be found for its doubly degenerate ground states. The family of Hamiltonians which we define, depend on 5 continuous parameters and the Majumdar-Ghosh model is a particular point in this parameter space. Like the Majumdar-Ghosh model, the doubly degenerate ground states of our models have a very simple structure, they are the product of entangled states on adjacent sites. In each of these states there is a non-zero staggered magnetization, which vanishes when we take their translation-invariant combination as the new ground states. At the Majumdar-Ghosh point, these entangled states become the spin-singlets pertaining to this model. We will also calculate in closed form the two point correlation functions, both for finite size of the chain and in the thermodynamic limit.Comment: 11 page

Rigidity of Determinantal Point Processes with the Airy, the Bessel and the Gamma Kernel

A point process is said to be rigid if for any bounded domain in the phase space, the number of particles in the domain is almost surely determined by the restriction of the configuration to the complement of our bounded domain. The main result of this paper is that determinantal point processes with the Airy, the Bessel and the Gamma kernels are rigid. The proof follows the scheme of Ghosh [6], Ghosh and Peres [7]: the main step is the construction of a sequence of additive statistics with variance going to zero.Comment: 10 page

Book review: Decentering Empire: Britain, India and the Transcolonial World

This article reviews the book: “Decentering Empire: Britain, India and the Transcolonial World”, by Durba Ghosh and Dane Kennedy

Introduction: Unrecorded Lives

When anthropology student (and later, novelist) Amitav Ghosh set out from Oxford to Egypt in 1980 to find a suitable subject for his research, he may not have suspected the impact the trip would have on his life. He succeeded in completing the required tome for his degree and then went on to write In an Antique Land (1992), an unusually constructed book that deals with themes of historical and cultural displacement, with alienation and something we might these days, under the influence of postcolonial theory, call subaltern cosmopolitanism. Others might recognize the genre in which Ghosh is writing as one we have all tried our hand at, in one form or another: a record of discomfort in confronting the inconsistencies of another person\u27s-the other person\u27s-reality. The book is hardly recognizable as a novel; nor is it simply a historical investigation, since it blends an anthropological record with a travelogue, a diary, and speculations. Within the parameters of history, Ghosh told one interviewer, I have tried to capture a story, a narrative, without attempting to write a historical novel. You may say, as a writer, I have ventured on a technical innovation (Dhawan 1999: 24). In India in Africa, Africa in India we are attempting a parallel innovation : using what we know of the past to inform our understanding of the present Indian Ocean world; examining today\u27s imaginative interpretations of India by Africans and Africa by Indians to speculate on how, historically, these regions understood each other. Ghosh gathered evidence relating to a Jewish merchant operating in the twelfth century in Aden, and he was seeking to document, more remarkably, the merchant\u27s barely recoverable Indian slave. In the process, Ghosh learns as much about the interpretation his visit gets from the Africans he meets as he does about the merchant Ben Yiju\u27s reception in India and the role of the slave Bomma in the world of Indian Ocean commerce seven hundred or so years ago-for Ghosh was as much an object of fascination to the Egyptians as they were to him. There has been a coming and going for centuries, sometimes enforced, sometimes enthusiastically entered into, and one might have thought that this would have made for greater understanding among the various parties. But exactly the opposite was the case when the young doctoral student sat across from the aged imam in the Egyptian village and was told by him to stop doing the strange things that the villagers had heard were done by Hindus. Did his people bury their dead, or cremate them, he was asked. Was he circumcised? Did they worship cows? Is there military service for all in India, as there is in Egypt? Why did they not purify (i .e., infibulate or circumcise) their women? In fact, the imam and his villagers seemed to encourage him to remain apart from them, making sure that the young interloper did not enjoy the sense of community that they created during Ramadan. As Ghosh puts it, to belong to that immense community was a privilege they had to re-earn every year, and the effort made them doubly conscious of the value of its boundaries (A. Ghosh 1992: 76)

The Minimum S-Divergence Estimator under Continuous Models: The Basu-Lindsay Approach

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical maximum likelihood based techniques. Recently Ghosh et al. (2013) proposed a general class of divergence measures for robust statistical inference, named the S-Divergence Family. Ghosh (2014) discussed its asymptotic properties for the discrete model of densities. In the present paper, we develop the asymptotic properties of the proposed minimum S-Divergence estimators under continuous models. Here we use the Basu-Lindsay approach (1994) of smoothing the model densities that, unlike previous approaches, avoids much of the complications of the kernel bandwidth selection. Illustrations are presented to support the performance of the resulting estimators both in terms of efficiency and robustness through extensive simulation studies and real data examples.Comment: Pre-Print, 34 page