Sofic Mean Dimension
نویسنده
چکیده
We introduce mean dimensions for continuous actions of countable sofic groups on compact metrizable spaces. These generalize the Gromov-LindenstraussWeiss mean dimensions for actions of countable amenable groups, and are useful for distinguishing continuous actions of countable sofic groups with infinite entropy.
منابع مشابه
Quantifier Extensions of Multidimensional Sofic Shifts
We define a pair of simple combinatorial operations on subshifts, called existential and universal extensions, and study their basic properties. We prove that the existential extension of a sofic shift by another sofic shift is always sofic, and the same holds for the universal extension in one dimension. However, we also show by a construction that universal extensions of twodimensional sofic ...
متن کاملSofic Mean Length
Given a length function L on the R-modules of a unital ring R, for any sofic group Γ, we define a mean length for every locally L-finite RΓ-module relative to a bigger RΓ-module. We establish an addition formula for the mean length. We give two applications. The first one shows that for any unital left Noetherian ring R, RΓ is stably direct finite. The second one shows that for any ZΓ-module M,...
متن کاملSofic Dimension for Discrete Measured Groupoids
For discrete measured groupoids preserving a probability measure we introduce a notion of sofic dimension that measures the asymptotic growth of the number of sofic approximations on larger and larger finite sets. In the case of groups we give a formula for free products with amalgamation over an amenable subgroup. We also prove a free product formula for measure-preserving actions.
متن کاملA Free Product Formula for the Sofic Dimension
It is proved that if G = G1 ∗G3 G2 is free product of probability measure preserving s-regular ergodic discrete groupoids amalgamated over an amenable subgroupoid G3, then the sofic dimension s(G) satisfies the equality s(G) = h(G01)s(G1) + h(G 0 2)s(G2) − h(G 0 3)s(G3) where h is the normalized Haar measure on G. Let G be a group. The sofic dimension of G is an asymptotic invariant that accoun...
متن کاملDynamique symbolique des systèmes 2D et des arbres infinis. (Symbolic dynamics on multidimensional systems and infinite trees)
This thesis is devoted to the study of subshifts, or symbolic dynamical systems, defined on some finitely presented monoids like Zd or the infinite binary tree. The main result concerning multidimensional subshifts establishes that any effective subshift of dimension d can be obtained by factor map and projective subaction of a subshift of finite type of dimension d+ 1. This result has many app...
متن کامل