139 research outputs found
Poisson cluster measures: Quasi-invariance, integration by parts and equilibrium stochastic dynamics
Abstract The distribution µ cl of a Poisson cluster process in X = R d (with i.i.d. clusters) is studied via an auxiliary Poisson measure on the space of configurations in X = n X n , with intensity measure defined as a convolution of the background intensity of cluster centres and the probability distribution of a generic cluster. We show that the measure µ cl is quasiinvariant with respect to the group of compactly supported diffeomorphisms of X and prove an integration-by-parts formula for µ cl . The corresponding equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms
Nambu-Poisson manifolds and associated n-ary Lie algebroids
We introduce an n-ary Lie algebroid canonically associated with a
Nambu-Poisson manifold. We also prove that every Nambu-Poisson bracket defined
on functions is induced by some differential operator on the exterior algebra,
and characterize such operators. Some physical examples are presented
Approximate Homomorphisms of Ternary Semigroups
A mapping between ternary semigroups will be
called a ternary homomorphism if . In this paper,
we prove the generalized Hyers--Ulam--Rassias stability of mappings of
commutative semigroups into Banach spaces. In addition, we establish the
superstability of ternary homomorphisms into Banach algebras endowed with
multiplicative norms.Comment: 10 page
Gauge-Invariant Quasi-Free States on the Algebra of the Anyon Commutation Relations
Let and let , . For and from , we define a function to be equal to if , and to if . Let , () be operator-valued distributions such that is the adjoint of . We say that , satisfy the anyon commutation relations (ACR) if for and for . In particular, for , the ACR become the canonical commutation relations and for , the ACR become the canonical anticommutation relations. We define the ACR algebra as the algebra generated by operator-valued integrals of , . We construct a class of gauge-invariant quasi-free states on the ACR algebra. Each state from this class is completely determined by a positive self-adjoint operator on the real space which commutes with any operator of multiplication by a bounded function . In the case ), we discuss the corresponding particle density . For , using a renormalization, we rigorously define a vacuum state on the commutative algebra generated by operator-valued integrals of . This state is given by a negative binomial point process. A scaling limit of these states as gives the gamma random measure, depending on parameter
Generalized ulam-hyers stability of C*-Ternary algebra n-Homomorphisms for a functional equation
Cluster point processes on manifolds
The probability distribution μ_cl of a general cluster point process in a Riemannian manifold X (with independent random clusters attached to points of a configuration with distribution μ) is studied via the projection of an auxiliary measure ˆμ in the space of configurations ˆ Γ = {(x,y)} ⊂ X × X, where x ∈ X indicates a cluster "centre" and y ∈ X represents a corresponding cluster relative to x. We show that the measure μ_cl is quasi-invariant with respect to the group Diff0(X) of compactly supported diffeomorphisms of X, and prove an integration-by-parts formula for μcl. The associated equilibrium stochastic dynamics is then constructed using the method of Dirichlet forms. General constructions are illustrated by examples including Euclidean spaces, Lie groups, homogeneous spaces, Riemannian manifolds of non-positive curvature and metric spaces
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