Related papers: Partition function loop series for a general graph…
We present a new expression for the partition function of refined Chern-Simons theory on $S^3$ with arbitrary gauge group, which is explicitly equal to $1$, when the coupling constant is zero. Using this form of partition function we show…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
The sum-product or belief propagation (BP) algorithm is a widely-used message-passing algorithm for computing marginal distributions in graphical models with discrete variables. At the core of the BP message updates, when applied to a…
The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing…
We compute the logarithmic asymptotics of the non-existence probability (and more generally the lower-tail probability) for a wide variety of combinatorial problems for a range of parameters in the `critical regime' between the regime…
An old problem in mathematical physics deals with the structure of the dispersion relation of the Schr\"odinger operator $-\Delta+V(x)$ in $R^n$ with periodic potential near the edges of the spectrum. A well known conjecture says that…
We apply to the Random Field Ising Model at zero temperature (T= 0) the perturbative loop expansion around the Bethe solution. A comparison with the standard epsilon-expansion is made, highlighting the key differences that make the new…
The graphs induced by partition logics allow a dual probabilistic interpretation: a classical one for which probabilities lie on the convex hull of the dispersion-free weights, and another one, suggested independently from the quantum Born…
We provide an exact expression of the moment of the partition function for random energy models of finite system size, generalizing an earlier expression for a grand canonical version of the discrete random energy model presented by the…
In this chapter a general mathematical framework for probabilistic theories of operationally understood circuits is laid out. Circuits are comprised of operations and wires. An operation is one use of an apparatus and a wire is a…
Given any task $\Pi$, Brandt's speedup theorem (PODC 2019) provides a mechanical way to design another task~$\Pi'$ on the same input-set as $\Pi$ such that, for any $t\geq 1$, $\Pi$ is solvable in $t$ rounds if and only if $\Pi'$ is…
Belief Propagation (BP) is a widely used approximation for exact probabilistic inference in graphical models, such as Markov Random Fields (MRFs). In graphs with cycles, however, no exact convergence guarantees for BP are known, in general.…
We introduce a general Bayesian framework for graph matching grounded in a new theory of exchangeable random permutations. Leveraging the cycle representation of permutations and the literature on exchangeable random partitions, we define,…
Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper,…
We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function $q(x)$ is computed at high orders in powers of $\tau=T_c-T$ and $H$. We find that none of…
We study the problem of assortative and disassortative partitions on random $d$-regular graphs. Nodes in the graph are partitioned into two non-empty groups. In the assortative partition every node requires at least $H$ of their neighbors…
Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences…
We provide an explicit formula for the limiting free energy density (log-partition function divided by the number of vertices) for ferromagnetic Potts models on uniformly sparse graph sequences converging locally to the d-regular tree for d…
Loopy belief propagation performs approximate inference on graphical models with loops. One might hope to compensate for the approximation by adjusting model parameters. Learning algorithms for this purpose have been explored previously,…
We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…