By Alexander Gorodnik
The effects verified during this e-book represent a brand new departure in ergodic conception and an important growth of its scope. conventional ergodic theorems interested by amenable teams, and trusted the life of an asymptotically invariant series within the staff, the ensuing maximal inequalities in keeping with masking arguments, and the transference precept. right here, Alexander Gorodnik and Amos Nevo boost a scientific common method of the evidence of ergodic theorems for a wide classification of non-amenable in the neighborhood compact teams and their lattice subgroups. basic common stipulations at the spectral conception of the crowd and the regularity of the averaging units are formulated, which suffice to assure convergence to the ergodic suggest. specifically, this procedure offers an entire option to the matter of creating suggest and pointwise ergodic theorems for the normal averages on semisimple algebraic teams and on their discrete lattice subgroups. in addition, an particular quantitative expense of convergence to the ergodic suggest is demonstrated in lots of cases.
The subject of this quantity lies on the intersection of numerous mathematical fields of primary value. those contain ergodic concept and dynamics of non-amenable teams, harmonic research on semisimple algebraic teams and their homogeneous areas, quantitative non-Euclidean lattice element counting difficulties and their program to quantity thought, in addition to equidistribution and non-commutative Diophantine approximation. Many examples and purposes are supplied within the textual content, demonstrating the usefulness of the implications established.
Read Online or Download The Ergodic Theory of Lattice Subgroups (AM-172) (Annals of Mathematics Studies) PDF
Similar Group Theory books
This monograph brings jointly my paintings in mathematical facts as i've got considered it during the lens of Jordan algebras. 3 technical domain names are to be obvious: functions to random quadratic types (sums of squares), the research of algebraic simplifications of maxi mum probability estimation of patterned covariance matrices, and a extra huge open mathematical exploration of the algebraic enviornment from which i've got drawn the implications utilized in the statistical difficulties simply pointed out.
The first aim of those lectures is to introduce a newbie to the finite dimensional representations of Lie teams and Lie algebras. in view that this aim is shared by means of a number of different books, we must always clarify during this Preface how our strategy differs, even supposing the capability reader can most likely see this larger by means of a brief flick through the ebook.
"A remarkably intelligible survey . . . good geared up, good written and intensely transparent all through. " — Mathematical ReviewsThis very good textual content, lengthy one among the best-written, so much skillful expositions of crew idea and its actual purposes, is directed essentially to complicated undergraduate and graduate scholars in physics, specifically quantum physics.
Additional resources for The Ergodic Theory of Lattice Subgroups (AM-172) (Annals of Mathematics Studies)