## Download The Ergodic Theory of Lattice Subgroups by Alexander Gorodnik PDF

By Alexander Gorodnik

ISBN-10: 0691141851

ISBN-13: 9780691141855

The consequences proven during this publication represent a brand new departure in ergodic idea and an important growth of its scope. conventional ergodic theorems keen on amenable teams, and depended on the life of an asymptotically invariant series within the staff, the ensuing maximal inequalities in accordance with overlaying arguments, and the transference precept. right here, Alexander Gorodnik and Amos Nevo enhance a scientific basic method of the evidence of ergodic theorems for a wide category of non-amenable in the neighborhood compact teams and their lattice subgroups. basic basic stipulations at the spectral thought of the crowd and the regularity of the averaging units are formulated, which suffice to assure convergence to the ergodic suggest. particularly, this method supplies 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. additionally, an specific quantitative expense of convergence to the ergodic suggest is verified in lots of cases.The subject of this quantity lies on the intersection of numerous mathematical fields of basic significance. those comprise ergodic thought 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 software to quantity idea, in addition to equidistribution and non-commutative Diophantine approximation. Many examples and functions are supplied within the textual content, demonstrating the usefulness of the implications demonstrated.