Group Theory

Download E-books The Ergodic Theory of Lattice Subgroups (AM-172) (Annals of Mathematics Studies) PDF

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.

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