Continuous hemigroups of probability measures on a Lie group

1982 ◽  
pp. 362-402 ◽  
Author(s):  
Eberhard Siebert
Keyword(s):  
Lie Group ◽  
Probability Measures

scholarly journals Convexity theorems for the gradient map on probability measures

2018 ◽  
Vol 5 (1) ◽  
pp. 133-145 ◽  
Author(s):  
Leonardo Biliotti ◽  
Alberto Raffero
Keyword(s):  
Lie Group ◽  
Kähler Manifold ◽  
Probability Measures ◽  
Kahler Manifold ◽  
Abelian Case ◽  
Real Submanifold ◽  
Reductive Lie Group

AbstractGiven a Kähler manifold (Z, J, ω) and a compact real submanifold M ⊂ Z, we study the properties of the gradient map associated with the action of a noncompact real reductive Lie group G on the space of probability measures on M. In particular, we prove convexity results for such map when G is Abelian and we investigate how to extend them to the non-Abelian case.

scholarly journals Moments of probability measures on a group

1981 ◽  
Vol 4 (1) ◽  
pp. 1-37 ◽  
Author(s):  
Herbert Heyer
Keyword(s):  
Topological Group ◽  
Banach Spaces ◽  
Lie Groups ◽  
Finite Groups ◽  
Lie Group ◽  
Probability Measures ◽  
Moment Conditions ◽  
New Developments ◽  
Large Numbers ◽  
Special Cases

New developments and results in the theory of expectatiors and variances for random variables with range in a topological group are presented in the following order (i) Introduction (2) Basic notions (3) The three series theorem in Banach spaces (4) Moment Conditions (5) Expectations and variances (6) A general three series theorem (7) The special cases of finite groups and Lie groups (8)The strong laws of large numbers on a Lie group (9) Further studies on moments of probability measures.

scholarly journals Hypergroups associated to harmonic NA groups

2002 ◽  
Vol 72 (2) ◽  
pp. 209-216 ◽  
Author(s):  
Bianca Di Blasio
Keyword(s):  
Compact Space ◽  
Lie Group ◽  
Probability Measures ◽  
Nilpotent Lie Group ◽  
Locally Compact ◽  
Structure Preserving ◽  
Borel Measures ◽  
Heisenberg Type ◽  
Convolution Structure ◽  
Solvable Extension

AbstractA harmonic NA group is a suitable solvable extension of a two-step nilpotent Lie group N of Heisenberg type by R+, which acts on N by anisotropic dilations. A hypergroup is a locally compact space for which the space of Borel measures has a convolution structure preserving the probability measures and satisfying suitable conditions. We describe a class of hypergroups associated to NA groups.

Construction of Levi processes on path spaces of Lie groups

2016 ◽  
Vol 19 (01) ◽  
pp. 1650002
Author(s):  
A. A. Kalinichenko
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Weak Limit ◽  
Convolution Semigroup ◽  
Path Space ◽  
Probability Measures ◽  
Compact Lie Group ◽  
Piecewise Constant ◽  
Finite Dimensional

Given a compact Lie group and a conjugate-invariant Levi process on it, generated by the operator [Formula: see text], we construct the Levi process on the path space of [Formula: see text], associated with the convolution semigroup [Formula: see text] of probability measures, where [Formula: see text] is the distribution of the Levi process on [Formula: see text] generated by [Formula: see text]. The constructed process is obtained as the weak limit of piecewise constant paths, which, as well as proving its existence and properties, provides finite-dimensional approximations of Chernoff type to the integrals with respect to its distribution.

Invariance groups and convergence of types of measures on Lie groups

1992 ◽  
Vol 112 (1) ◽  
pp. 91-108 ◽  
Author(s):  
S. G. Dani
Keyword(s):  
Probability Measure ◽  
Lie Groups ◽  
Lie Group ◽  
Weak Topology ◽  
Probability Measures ◽  
Affine Subspace ◽  
Invariance Groups ◽  
Connected Lie Group

Let G be a connected Lie group and let {λi} be a sequence of probability measures on G converging (in the usual weak topology) to a probability measure λ. Suppose that {αi} is a sequence of affine automorphisms of G such that the sequence {αi,(λi)} also converges, say to a probability measure μ. What does this imply about the sequence {αi}? It is a classical observation that if G = ℝn for some n, and neither of λ and μ is supported on a proper affine subspace of ℝn, then under the above condition, {αi} is relatively compact in the group of all affine automorphisms of ℝn.

On the space of ergodic invariant measures of unipotent flows

1995 ◽  
Vol 15 (1) ◽  
pp. 149-159 ◽  
Author(s):  
Shahar Mozes ◽  
Nimish Shah
Keyword(s):  
Lie Group ◽  
Invariant Measures ◽  
Closed Orbit ◽  
Convergent Sequence ◽  
Discrete Subgroup ◽  
Probability Measures ◽  
Unipotent Flows

AbstractLet G be a Lie group and Γ be a discrete subgroup. We show that if {μn} is a convergent sequence of probability measures on G/Γ which are invariant and ergodic under actions of unipotent one-parameter subgroups, then the limit μ of such a sequence is supported on a closed orbit of the subgroup preserving it, and is invariant and ergodic for the action of a unipotent one-parameter subgroup of G.

LIFTING THE FUNCTOR ITO THE CATEGORY OF UNIFORM SPACES

2020 ◽  
Vol 4 (1) ◽  
pp. 29-39
Author(s):  
Dilrabo Eshkobilova ◽  
Keyword(s):  
Compact Support ◽  
Probability Measures ◽  
Uniform Spaces ◽  
Continuous Maps ◽  
Uniformly Continuous

Uniform properties of the functor Iof idempotent probability measures with compact support are studied. It is proved that this functor can be lifted to the category Unif of uniform spaces and uniformly continuous maps

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