Related papers: Loop corrections for hard spheres in Hamming space
We present an analytical approach for describing spectrally constrained maximum entropy ensembles of finitely connected regular loopy graphs, valid in the regime of weak loop-loop interactions. We derive an expression for the leading two…
We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n -> oo, d -> oo, d/n=delta. The problem is relevant for coding theory. We find a solution to the…
We numerically calculate the configurational entropy S_conf of a binary mixture of hard spheres, by using a perturbed Hamiltonian method trapping the system inside a given state, which requires less assumptions than the previous methods…
We introduce a novel method for computing entanglement entropy across surfaces in Loop Quantum Gravity by employing techniques from quantum error correcting codes. In this construction, the redundancy encoded in the gauge invariant subspace…
Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the…
Black hole thermodynamics suggests that the maximum entropy that can be contained in a region of space is proportional to the area enclosing it rather than its volume. I argue that this follows naturally from loop quantum gravity and a…
This paper develops a non-asymptotic approach to mean field approximations for systems of $n$ diffusive particles interacting pairwise. The interaction strengths are not identical, making the particle system non-exchangeable. The marginal…
There is an increasing interest in scaling tensor network methods through belief propagation (BP), as well as increasing the accuracy of BP through tensor network methods. We develop a unification framework that takes an arbitrary graphical…
Data association, the problem of reasoning over correspondence between targets and measurements, is a fundamental problem in tracking. This paper presents a graphical model formulation of data association and applies an approximate…
Given a set of discrete probability distributions, the minimum entropy coupling is the minimum entropy joint distribution that has the input distributions as its marginals. This has immediate relevance to tasks such as entropic causal…
We study the probability distribution of entanglement in the Quantum Symmetric Simple Exclusion Process, a model of fermions hopping with random Brownian amplitudes between neighboring sites. We consider a protocol where the system is…
Under high cylindrical confinement, segments of ring polymers can be localized along the long axis of the cylinder by introducing internal loops within the ring polymer. The emergent organization of the polymer segments occurs because of…
One-dimensional multi-component Fermi or Bose systems with strong zero-range interactions can be described in terms of local exchange coefficients and mapping the problem into a spin model is thus possible. For arbitrary external confining…
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…
This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…
Entanglement entropy under a particle bipartition provides complementary information to mode entanglement as it is sensitive to interactions and particle statistics at leading order and does not depend on any externally imposed length…
The entanglement and R\'{e}nyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT…
Entanglement entropy for a spatial partition of a quantum system is studied in theories which admit a dual description in terms of the anti-de Sitter (AdS) gravity one dimension higher. A general proof of the holographic formula which…
We consider the general problem of finding the minimum weight $\bm$-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP)…
We derive bounds for the ball $L_p$-discrepancies in the Hamming space for $0<p<\infty$ and $p=\infty$. Sharp estimates of discrepancies have been obtained for many spaces such as the Euclidean spheres and more general compact Riemannian…