Related papers: Dynkin's isomorphism without symmetry

Based on collection of bijections, variable and function are extended into ``isomorphic variable'' and ``dual-variable-isomorphic function'', then mean values such as arithmetic mean and mean of a function are extended to ``isomorphic…

We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under…

We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general…

We construct a generalization of the theory of symmetric functions involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal…

The main topic of these notes are Markov loops, studied in the context of continuous time Markov chains on discrete state spaces. We refer to [1] and [2] for the short "history" of the subject. In contrast with these references, symmetry is…

In this lectures various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. While applying asymptotic methods as a rule the following situation…

The theory of non symmetric Dirichlet forms is generalized to the non abelian setting, also establishing the natural correspondences among Dirichlet forms, sub-Markovian semigroups and sub-Markovian resolvents within this context. Examples…

The asymptotic expansion of $n$-dimensional cyclic integrals was expressed as a series of functionals acting on the symmetric function involved in the cyclic integral. In this article, we give an explicit formula for the action of these…

An afinne-invariant view of generating functions of symplectic transformations of an affine symplectic space is discussed. More generally, it works for symmetric symplectic spaces. The note is completely elementary, but it yields some nice…

In this work we construct an infinite class of four-point functions for massless higher-spin fields in flat space that are consistent with the gauge symmetry. In the Lagrangian picture, these reflect themselves in a peculiar non-local…

We extend the concept of Lyapunov 1-forms for the case of diffu- sion processes to study its asymptotic behavior. We give some examples and a condition for the existence of these objects.

Consider an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. In order to establish concentration properties for nonlinear functions $Z(A)$, it is standard to appeal to functional inequalities like Poincar\'e or…

We rigorously establish the asymptotic equivalence between the height function of interacting dimers on the square lattice and the massless Gaussian free field. Our theorem explains the microscopic origin of the sine-Gordon field theory…

We give a systematic and thorough study of geometric notions and results connected to Minkowski's measure of symmetry and the extension of the well-known Minkowski functional to arbitrary, not necessarily symmetric convex bodies K on any…

In this article we address the question of asymptotic symmetry of massless scalar field at null infinity. We slightly generalize notion of asymptotic symmetry in order to make sense for the theory without gauge symmetry. Derivations of the…

We introduce a simple representation for isotropic spherical random fields and we discuss how it allows to discuss different notions of sparsity under isotropy. We also show how a suitable construction of sparse fields can mimic well the…

We construct harmonic functions in the quarter plane for discrete Laplace operators. In particular, the functions are conditioned to vanish on the boundary and the Laplacians admit coefficients associated with transition probabilities of…

Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…

Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…

We describe quantum symmetries associated with the F4 Dynkin diagram. Our study stems from an analysis of the (Ocneanu) modular splitting equation applied to a partition function which is invariant under a particular congruence subgroup of…