Related papers: Random-Cluster Representation of the Ashkin-Teller…

We attempt to generalize the $p$-modular representation theory of finite groups to finite transporter categories, which are regarded as generalized groups. We shall carry on our tasks through modules of transporter category algebras, a type…

We give a characterization of $n$-cluster tilting subcategories of representation-directed algebras based on the $n$-Auslander-Reiten translations. As an application we classify acyclic Nakayama algebras with homogeneous relations which…

Given a category C of a combinatorial nature, we study the following fundamental question: how does the combinatorial behavior of C affect the algebraic behavior of representations of C? We prove two general results. The first gives a…

We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree…

In the strong coupling limit the partition function of SU(2) gauge theory can be reduced to that of the continuous spin Ising model with nearest neighbour pair-interactions. The random cluster representation of the continuous spin Ising…

Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…

Let $G$ be a finite group. In the first part of the paper we develop further the foundations of the youngly introduced glider representation theory. Glider representations encompass filtered modules over filtered rings and as such carry…

For a random intersection graph with a power law degree sequence having a finite mean and an infinite variance we show that the global clustering coefficient admits a tunable asymptotic distribution.

In this paper we provide an extension of the theory of descent of Ginzburg-Rallis- Soudry to the context of essentially self-dual representations, that is representations which are isomorphic to the twist of their own contragredient by some…

The prevailing graph neural network models have achieved significant progress in graph representation learning. However, in this paper, we uncover an ever-overlooked phenomenon: the pre-trained graph representation learning model tested…

We suggest a generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the…

We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…

Random Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix ensembles defined on k-fold tensor products of…

We prove Griffiths inequalities for the $O(N)$-spin model with inhomogeneous coupling constants and external magnetic field for any $N\geq 2$. This is achieved by using a representation of $O(N)$-spins in terms of random paths that reduces…

We study the balance of $G$-gain graphs, where $G$ is an arbitrary group, by investigating their adjacency matrices and their spectra. As a first step, we characterize switching equivalence and balance of gain graphs in terms of their…

Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…

In this short review we introduce group field theory, a particular class of random tensor models, which represents nowadays one of the candidates for a fundamental theory of quantum gravity. We insist on the combinatorial richness of…

For the Ising model, the spin magnetization transition is equivalent to the percolation transition of Fortuin-Kasteleyn clusters; this result remains valid also for the conventional continuous spin Ising model. The investigation of more…

Cluster-Weighted Modeling (CWM) is a flexible mixture approach for modeling the joint probability of data coming from a heterogeneous population as a weighted sum of the products of marginal distributions and conditional distributions. In…

We describe random loop models and their relations to a family of quantum spin systems on finite graphs. The family includes spin 1/2 Heisenberg models with possibly anisotropic spin interactions and certain spin 1 models with…