Related papers: A direct proof of Jauregui-Tsallis' conjecture
We obtain a multidimensional Tauberian theorem for Laplace transforms of Gelfand-Shilov ultradistributions. The result is derived from a Laplace transform characterization of bounded sets in spaces of ultradistributions with supports in a…
In this paper some new characterizing theorems of exponential distribution based on order statistics are presented. Some existing results are generalized and the open conjecture by Arnold and Villasenor is solved.
We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding $q$-supercongruence. Similar $q$-supercongruences are established for binomial coefficients and the Ap\'{e}ry numbers, by means of a general…
We prove a compositional refinement of the Delta conjecture (rise version) of Haglund, Remmel and Wilson (2018) for $\Delta_{e_{n-k-1}}'e_n$ which was stated by D'Adderio, Iraci and Vanden Wyngaerd (2020) in terms of Theta operators.
A formal correspondence between the q-distribution obtained from the Tsallis entropy and non-maxwellian distributions obtained from the Boltzmann-Gibbs entropy is afforded.
We establish effective equidistribution theorems, with a polynomial error rate, for orbits of unipotent subgroups in quotients of quasi-split, almost simple Linear algebraic groups of absolute rank 2. As an application, inspired by the…
Many common probability distributions in statistics like the Gaussian, multinomial, Beta or Gamma distributions can be studied under the unified framework of exponential families. In this paper, we prove that both R\'enyi and Tsallis…
We provide numerical indications of the $q$-generalised central limit theorem that has been conjectured (Tsallis 2004) in nonextensive statistical mechanics. We focus on $N$ binary random variables correlated in a {\it scale-invariant} way.…
We study the joint distribution of values of a pair consisting of a quadratic form $q$ and a linear form $\mathbf l$ over the set of integral vectors, a problem initiated by Dani-Margulis (1989). In the spirit of the celebrated theorem of…
It is argued that polydispersed systems like colloids provide a direct example where Tsallis' statistical distribution is useful for describing the heirarchical nature of the system based on particle size.
In this note, we prove a conjecture proposed by Tao Zhang, Shuxing Li, Tao Feng and Gennian Ge, IEEE Transaction on Information Theory, vol. 60, no. 5, May 2014. This conjecture is about the cross correlation distribution of ternary…
The aim of this expository note is to prove that any $1$-subgaussian random vector is dominated in the convex ordering by a universal constant times a standard Gaussian vector. This strengthens Talagrand's celebrated subgaussian comparison…
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
Euler turbulence has been experimentally observed to relax to a metaequilibrium state that does not maximize the Boltzmann entropy, but rather seems to minimize enstrophy. We show that a recent generalization of thermodynamics and…
New results on comparison of distributions of Gaussian quadratic forms are presented
We give a new proof of the sharp symmetrized form of Talagrand's transport-entropy inequality. Compared to stochastic proofs of other Gaussian functional inequalities, the new idea here is a certain coupling induced by time-reversed…
In a recent letter (EPL, 104 (2013) 60003) we suggested a way to avoid divergences inherent to the formulation of nonextensive statistical mechanics. They can be eliminated via the use of a q-Laplace transformation, which was illustrated…
Using quantization techniques, we show that the $\delta$-invariant of Fujita-Odaka coincides with the optimal exponent in certain Moser-Trudinger type inequality. Consequently we obtain a uniform Yau-Tian-Donaldson theorem for the existence…
The Shuffle Theorem of Carlsson and Mellit gives a combinatorial expression for the bigraded Frobenius characteristic of the ring of diagonal harmonics, and the Delta Conjecture of Haglund, Remmel and the second author provides two…
We show that within classical statistical mechanics it is possible to naturally derive power law distributions which are of Tsallis type. The only assumption is that microcanonical distributions have to be separable from of the total system…