JournalscmhVol. 85, No. 3pp. 647–704

The large sieve and random walks on left cosets of arithmetic groups

  • Florent Jouve

    Université Paris-Sud 11, Orsay, France
The large sieve and random walks on left cosets of arithmetic groups cover
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Abstract

Building on Kowalski’s work on random walks on the groups SL(n,ℤ) and Sp(2g,ℤ), we consider similar problems (we try to estimate the probability with which, after k steps, the matrix obtained has a characteristic polynomial with maximal Galois group or has no nonzero squares among its entries) for more general classes of sets: in GL(n,A), where A is a subring of ℚ containing ℤ that we specify, we perform a random walk on the set of matrices with fixed determinant D ∈ A×. We also investigate the case where the set involved is any of the two left cosets of the special orthogonal group SO(n,m)(ℤ) with respect to the spinorial kernel Ω(n,m)(ℤ).

Cite this article

Florent Jouve, The large sieve and random walks on left cosets of arithmetic groups. Comment. Math. Helv. 85 (2010), no. 3, pp. 647–704

DOI 10.4171/CMH/207