Related papers: Construction and limit theorems for supCAR fields

In this work, we introduce a random field in view of natural image modeling, obtained as a limit of sequences of dead leaves models, when considering arbitrarily small or big objects. The dead leaves model, introduced by the Mathematical…

Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…

Using a generalization of complexes, called 2-complexes, this paper defines and analyzes new Sobolev spaces of matrix fields and their interrelationships within a commuting diagram. These spaces have very weak second-order derivatives. An…

In this work, families of kinks are analytically identified in multifield theories with either polynomial or deformed sine-Gordon-type potentials. The underlying procedure not only allows us to obtain analytical solutions for these models,…

In this long survey article we show that the theory of elliptic and hyperelliptic curves can be extended naturally to all superelliptic curves. We focus on automorphism groups, stratification of the moduli space $\mathcal{M}_g$, binary…

The quotient hyperfield is a landmark on the borderline of fields and hyperfields. In this paper, which is the second part of our previously published paper, all the hyperfields of order 7 are constructed, enumerated and presented, in the…

In this paper we investigate the possible supersymmetric extensions for the massive (bi)gravity theories in the lowest non-trivial order. For this purpose we construct the cubic interaction vertices for massive spin-2 and one or two massive…

The projection construction has been used to construct semifields of odd characteristic using a field and a twisted semifield [Commutative semifields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187--196]. We…

In this paper we study the convergence in distribution and the local limit theorem for the partial sums of linear random fields with i.i.d. innovations that have infinite second moment and belong to the domain of attraction of a stable law…

This paper develops new limit theory for data that are generated by networks or more generally display cross-sectional dependence structures that are governed by observable and unobservable characteristics. Strategic network formation…

In this paper we investigate cumulative hierarchies of functions on structures, or cumulative powers, and study their properties. Particularly, we show how they extend the preservation phenomena of reduced powers, direct powers and…

A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…

We address the scaling limits of random curves arising from, e.g., planar lattice models, especially in rough domains. The well-known precompactness conditions of Kemppainen and Smirnov show that certain crossing probability estimates…

In the paper we present simple examples of linear random fields defined on $\ZZ^2$ and $\ZZ^3$ which exhibit the scaling transition phenomenon. These examples lead to more general definition of the scaling transition and allow to understand…

We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…

We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation".…

We discuss finite local extensions of quantum field theories in low space time dimensions in connection with categorical structures and the question of modular invariants in conformal field theory, also touching upon purely mathematical…

We obtain a complete classification of hypercomplex manifolds, on which a compact group of automorphisms acts transitively. The description of the spaces as well as the proofs of our results use only the structure theory of reductive…

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k =…

The classification of emergent spinor fields according to modified bilinear covariants is scrutinized, in spacetimes with nontrivial topology, which induce inequivalent spin structures. Extended Clifford algebras, constructed by equipping…