Related papers: A Statistical-Physics Refinement of Soft Covering
The statistical mechanical partition function can be used to construct different forms of phase space distributions not restricted to the Gibbs-Boltzmann factor. With a generalised Lorentzian both the Kappa-Bose and Kappa-Fermi partition…
Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is…
In many scientific problems, researchers try to relate a response variable $Y$ to a set of potential explanatory variables $X = (X_1,\dots,X_p)$, and start by trying to identify variables that contribute to this relationship. In statistical…
We consider the one-dimensional partially asymmetric exclusion model with open boundaries. The model describes a system of hard-core particles that hop stochastically in both directions with different rates. At both boundaries particles are…
A full treatment for the scattering of an arbitrary number of bosons through a Bell multiport beam splitter is presented that includes all possible output arrangements. Due to exchange symmetry, the event statistics differs dramatically…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…
We study a variant of unequal error protection in channel coding, where the message bit string is divided into a finite number of blocks and the maximization objective is a weighted sum of per-block decoding success probabilities. The…
The number partitioning problem consists of partitioning a sequence of positive numbers ${a_1,a_2,..., a_N}$ into two disjoint sets, ${\cal A}$ and ${\cal B}$, such that the absolute value of the difference of the sums of $a_j$ over the two…
We discuss the implementation of physically meaningful branching ratios between the CRD and PRD contributions to the emissivity of a polarized multi-term atom in the presence of both inelastic and elastic collisions. Our derivation is based…
We study a paradigm of coding for compression of the natural numbers via the zeta distribution and develop a statistical-mechanical interpretation, both in terms of Hagedorn systems and a Bose gas with energy levels given by logarithms of…
The statistical mechanics of particles that populate indistinguishable energy sub-states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where for a given degeneracy,…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications and data storage systems. SC codes are constructed by partitioning an…
In the present letter a method to find a proper expression for the force distribution inside a granular sample in static equilibrium is proposed. The method is based in statistical mechanics and the force distribution is obtained by…
We investigate the upper tail distribution of the partition function of the directed polymer in a random environment on $\mathbb Z^d$ in the weak disorder phase. We show that the distribution of the infinite volume partition function…
The behavior of the self diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare…
Recent measurements of resonance widths for low-energy neutron scattering off heavy nuclei show large deviations from the standard Porter-Thomas distribution. We propose a new resonance width distribution based on the random matrix theory…
The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by…
Although exchangeable processes from Bayesian nonparametrics have been used as a generating mechanism for random partition models, we deviate from this paradigm to explicitly incorporate clustering information in the formulation of our…
Using high-resolution direct numerical simulations, the height and Reynolds number dependence of higher-order statistics of the energy dissipation rate and local enstrophy are examined in incompressible, fully-developed turbulent channel…
In the critical beta-splitting model of a random $n$-leaf rooted tree, clades are recursively split into sub-clades, and a clade of $m$ leaves is split into sub-clades containing $i$ and $m-i$ leaves with probabilities $\propto 1/(i(m-i))$.…