C. R. E. Raja

Distal actions and shifted convolution property

A locally compact group G is said to have shifted convolution property (abbr. as SCP) if for every regular Borel probability measure µ on G, either supx∈G µn(Cx) → 0 for all compact subsets C of G, or there exist x ∈ G and a compact subgroup K normalised by x such that µnx−n → ωK, the normalised Haar measure on K. We first consider distality of factor actions of distal actions. It is shown that this holds in particular for factors by compact groups invariant under the action and for factors by the connected component of the identity. We then characterize groups having SCP in terms of a readily verifiable condition on the conjugation action (pointwise distality). This gives some interesting corollaries to distality of certain actions and Choquet-Deny measures which actually motivated SCP and pointwise distal groups. We also relate distality of actions on groups to that of the extensions on the space of probability measures.

Some Properties of Distal Actions on Locally Compact Groups

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We also show that a compactly generated locally compact group of polynomial growth has a compact normal subgroup

A Note on Tortrat Groups

K

A Stochastic Difference Equation with Stationary Noise on Groups

such that

Expansive automorphisms of totally disconnected, locally compact groups

G/K

Polynomial Growth, Recurrence and Ergodicity for Random Walks on Locally Compact Groups and Homogeneous Spaces

is distal and the conjugacy action of

Classical theorems of probability on Gelfand pairs—Khinchin’s theorems and Cramér’s theorem

G

On Classes of p-adic Lie Groups

on

Operator Semi-Selfdecomposable Measures and Related Nested Subclasses of Measures on Vector Spaces

K

Factorisation Theorems for T-decomposable Measures on Groups

is ergodic; moreover, if