相关论文: Permutation Invariant Statistics, Duality and Simp…

A fundamental pillar of quantum mechanics concerns indistinguishable quantum particles. In three dimensions they may be classified into fermions or bosons, having, respectively, antisymmetric or symmetric wave functions under particle…

Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving…

In the last decade a huge amount of articles has been published studying pattern avoidance on permutations. From the point of view of enumeration, typically one tries to count permutations avoiding certain patterns according to their…

We present an exact scheme of bosonization for anyons (including fermions) in the two-dimensional manifold of the quantum Hall fluid. This gives every fractional quantum Hall phase of the electrons one or more dual bosonic descriptions. For…

By analyzing the BCS-BEC crossover, I found that because of the pairing interactions,a continuous family of quantum statistics interpolating between fermions and bosons is possible, although it seems incapable to construct reasonable wave…

Gentile statistics describes fractional statistical systems in the occupation number representation. Anyon statistics researches those systems in the winding number representation. Both of them are intermediate statistics between…

We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…

We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…

We review a recent development at the interface between discrete mathematics on one hand and probability theory and statistics on the other, specifically the use of Markov chains and their boundary theory in connection with the asymptotics…

Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non- canonical transformations in general also change the statistics of the operators involved. In…

Consider the regular representation of the sum over all permutations weighted by the sum of their descent, inversion, and fixed point multinomials. We compute the spectrum and the multiplicities of its elements of that matrix. Note that…

Permutation tableaux are combinatorial objects related with permutations and various statistics on them. They appeared in connection with total positivity in Grassmannians, and stationary probabilities in a PASEP model. In particular they…

Operators, refered to as k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of two noncommuting quon algebras. The deformation parameters for these quon algebras are roots of…

We study statistical signatures of composite bosons made of two fermions using a new many-body approach. Extending number-states to composite bosons, two-particle correlations as well as the dispersion of the probability distribution are…

We present a theory of particles, obeying intermediate statistics ("anyons"), interpolating between Bosons and Fermions, based on the principle of Detailed Balance. It is demonstrated that the scattering probabilities of identical particles…

New inference methods for the multivariate coefficient of variation and its reciprocal, the standardized mean, are presented. While there are various testing procedures for both parameters in the univariate case, it is less known how to do…

One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the last method. We consider the Poisson and binomial distributions in detail to illustrate a group invariance…

The idea that a system obeying interpolating statistics can be described by a deformed oscillator algebra has been an outstanding issue. This original concept introduced long ago by Greenberg is the motivation for this investigation. We…

Overparametrized models can exhibit an excellent generalization performance, although they should be prone to overfitting according to classical statistical theory. The discovery of the "double descent", indicating that the generalization…

We consider the relation between various permutation statistics and properties of permutation tableaux. We answer some of the questions of Steingrimsson and Williams (math.CO/0507149), in particular, on the distribution of the bistatistic…