The author obtains some classification result for the mapping class groups of compact
orientable surfaces in terms of measure equivalence. In particular, the mapping class groups …

The paper contains a description of the KMS weights for the one-parameter action on the
reduced C⁎-algebra of a second countable locally compact Hausdorff étale groupoid …

We prove pointwise and maximal ergodic theorems for probability-measure-preserving
(PMP) actions of any countable group, provided it admits an essentially free, weakly mixing …

We consider the harmonic measure on the Gromov boundary of a non-amenable hyperbolic
group defined by a finite range random walk on the group, and study the corresponding orbit …

We completely classify the Kubo–Martin–Schwinger (KMS) states for the gauge action on a
C*-algebra associated with a rational function R introduced in our previous work. The gauge …

We investigate the factor types of the extremal KMS states for the preferred dynamics on the
Toeplitz algebra and the Cuntz–Krieger algebra of a strongly connected finite k k-graph. For …

In this paper, we consider non-standard dynamics on the C∗-algebra associated with a
higher-rank graph Λ. These dynamics were first introduced by McNamara in his thesis, and …

We present a general new method for constructing pointwise ergodic sequences on
countable groups which is applicable to amenable as well as to non-amenable groups and …

We prove that the crossed product C*-algebra C* r (Γ,∂ Γ) of a free group Γ with its
boundary∂ Γ sits naturally between the reduced group C*-algebra C* rΓ and its injective …

We define k-dimensional digraphs and initiate a study of their spectral theory. The
kdimensional digraphs can be viewed as generating graphs for small categories called k …