Related papers: Spatial mixing and approximate counting for Potts …
One of the most important recent developments in the complexity of approximate counting is the classification of the complexity of approximating the partition functions of antiferromagnetic 2-spin systems on bounded-degree graphs. This…
For $\Delta \ge 5$ and $q$ large as a function of $\Delta$, we give a detailed picture of the phase transition of the random cluster model on random $\Delta$-regular graphs. In particular, we determine the limiting distribution of the…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
We compute the partition function of the $q$-states Potts model on a random planar lattice with $p\leq q$ allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit,…
The maximum energy of the EPR model on a weighted graph is known to be upper-bounded by the sum of the total weight and the value of maximum-weight fractional matching~(MWFM). Recently, Apte, Parekh and Sud~(APS) conjecture that the bound…
A flip of a graph is obtained by complementing the edge relation within a set of vertices. Flips are typically used to separate vertices in a graph, by increasing the distances between them. We show that in $K_{t,t}$-free graphs, every…
A widely-used operation on graphs is local clustering, i.e., extracting a well-characterized community around a seed node without the need to process the whole graph. Recently local motif clustering has been proposed: it looks for a local…
We revisit classical bounds of M. E. Fisher on the ferromagnetic Ising model, and show how to efficiently use them on an arbitrary given graph to rigorously upper-bound the partition function, magnetizations, and correlations. The results…
On locally tree-like random graphs, we relate the random cluster model with external magnetic fields and $q\geq 2$ to Ising models with vertex-dependent external fields. The fact that one can formulate general random cluster models in terms…
Using the Fundamental-Measure Density Functional Theory, we have studied theoretically the phase behavior of extremely confined mixtures of parallel hard squares in slit geometry. The pore width is chosen such that configurations consisting…
We consider Potts model hypersurfaces defined by the multivariate Tutte polynomial of graphs (Potts model partition function). We focus on the behavior of the number of points over finite fields for these hypersurfaces, in comparison with…
We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie…
Is Fully Polynomial-time Randomized Approximation Scheme (FPRAS) for a problem via an MCMC algorithm possible when it is known that rapid mixing provably fails? We introduce several weight-preserving maps for the eight-vertex model on…
The increasing availability of network data has driven the development of advanced statistical models specifically designed for metric graphs, where Gaussian processes play a pivotal role. While models such as Whittle-Mat\'ern fields have…
A finite dynamical system (FDS) is a system of multivariate functions over a finite alphabet, that is typically used to model a network of interacting entities. The main feature of a finite dynamical system is its interaction graph, which…
In this article we investigate a problem within Dempster-Shafer theory where 2**q - 1 pieces of evidence are clustered into q clusters by minimizing a metaconflict function, or equivalently, by minimizing the sum of weight of conflict over…
We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is…
Downsampling produces coarsened, multi-resolution representations of data and it is used, for example, to produce lossy compression and visualization of large images, reduce computational costs, and boost deep neural representation…
An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the…
Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs.…