Randomness in Diophantine approximation
Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015
Location: MSRI: Simons Auditorium
counting points on a lattice
unimodular lattices
asymptotic formulas
Borel sets
Siegel transform
central limit theorem
37Lxx - Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx]
11Jxx - Diophantine approximation, transcendental number theory [See also 11K60]
14236
We discuss the problem of counting solutions of Diophantine inequalities. While a general asymptotic formula for the counting function has been established by W. Schmidt, finer statistical properties of this function are still not well understood. We investigate its limiting distribution and establish the central limit theorem in this context. This is a joint work with Anish Ghosh.
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14236
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