Related papers: The Polya Urn: Limit Theorems, Polya Divergence, M…

There are two kinds of Tsallis-probability distributions: heavy tail ones and compact support distributions. We show here, appealing to functional analysis' tools, that for lower bound Hamiltonians only the first type guarantees a maximum…

We consider the theory of algebraically closed fields of characteristic zero with multivalued operations $x\mapsto x^r$ (raising to powers). It is in fact the theory of equations in exponential sums. In an earlier paper we have described…

In this paper we show how to extend the Sample-Path Large Deviation Principle for the urn model of Hill, Lane and Sudderth to the case in which the increment of the urn is not a binary variable. In particular, we sketch how to modify the…

Convex operational models (COMs) are considered as great extrapolations to larger settings of any statistical theory. In this article we generalize the maximum entropy principle (MaxEnt) of Jaynes' to any COM. After expressing Max-Ent in a…

Suppose an urn contains initially any number of balls of two colours. One ball is drawn randomly and then put back with $\alpha$ balls of the same colour and $\beta$ balls of the opposite colour. Both cases, $\beta=0$ and $\beta>0$ are well…

We consider the unique measure of maximal entropy of an automorphism of a compact K{\"a}hler manifold with simple action on cohomology. We show that it is exponentially mixing of all orders with respect to H{\"o}lder observables. It follows…

We consider planar Coulomb systems consisting of a large number $n$ of repelling point charges in the low temperature regime, where the inverse temperature $\beta$ grows at least logarithmically in $n$ as $n \longrightarrow \infty$, i.e.,…

We prove that the solution of the Kac analogue of Boltzmann's equation can be viewed as a probability distribution of a sum of a random number of random variables. This fact allows us to study convergence to equilibrium by means of a few…

Although compartmental dynamical systems are used in many different areas of science, model selection based on the maximum entropy principle (MaxEnt) is challenging because of the lack of methods for quantifying the entropy for this type of…

For a wide range of entropy measures, easy calculation of equilibria is possible using a principle of Game Theoretical Equilibrium related to Jaynes Maximum Entropy Principle. This follows previous work of the author and relates to works of…

For a compact convex set $K$ and a Poisson point process $\eta$, the union of all Voronoi cells with a nucleus in $K$ is the Poisson-Voronoi approximation of $K$. Lower and upper bounds for the variance and a central limit theorem for the…

We extend the well-known Rainwater-Simons convergence theorem to various generalized convergence methods such as strong matrix summability, statistical convergence and almost convergence. In fact we prove these theorems not only for…

We combine two of Igusa's conjectures with recent semi-continuity results by Musta\c{t}\u{a} and Popa to form a new, natural conjecture about bounds for exponential sums. These bounds have a deceivingly simple and general formulation in…

Let $K$ be a smooth convex set with volume one in $\BBR^d$. Choose $n$ random points in $K$ independently according to the uniform distribution. The convex hull of these points, denoted by $K_n$, is called a {\it random polytope}. We prove…

We obtain the analogue of the classical result by Erd\"os and Kac on the limiting distribution of the maximum of partial sums for exchangeable random variables with zero mean and variance one. We show that, if the conditions of the central…

We prove matching asymptotic lower and upper bounds on the variances of the intrinsic volumes and the number of $k$-faces of $d$-dimensional random beta-polytopes. Using Stein's methods, we establish central limit theorems for the intrinsic…

This is a research endeavor in two parts. We study a class of balanced urn schemes on balls of two colours (say white and black). At each drawing, a sample of size $m\ge 1$ is drawn from the urn, and ball addition rules are applied. We…

We give an analytic version of the injectivity theorem by using multiplier ideal sheaves, and prove some extension theorems for the adjoint bundle of dlt pairs. Moreover, by combining techniques of the minimal model program, we obtain some…

In this paper, under mild assumptions, we derive a law of large numbers, a central limit theorem with an error estimate, an almost sure invariance principle and a variant of Chernoff bound in finite-state hidden Markov models. These limit…

The method of maximum entropy (ME) is extended to address the following problem: Once one accepts that the ME distribution is to be preferred over all others, the question is to what extent are distributions with lower entropy supposed to…