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Journals and Conferences
We give a characteristic q > 0 analogue of the logarithm laws of Sullivan and Kleinbock-Margulis, and derive some corollaries in the diophantine theory of Laurent series over finite fields.
We prove quantitative recurrence and large deviations results for the Teichmuller geodesic flow on the moduli space Qg of holomorphic unitarea quadratic differentials on a compact genus g ≥ 2 surface.
We investigate the asymptotic uniqueness of the maximal order statistic of X1, X2, . . . , Xn, i.i.d. positive integer random variables, by casting the problem in a balls in boxes setting. We give a… (More)
We apply some of the ideas of the Ph.D. Thesis of G. A. Margulis [Mar70] to Teichmüller space. Let X be a point in Teichmüller space, and let BR(X) be the ball of radius R centered at X (with… (More)
We prove a polynomial upper bound on the deviation of er-godic averages for almost all directional flows on every translation surface , in particular, for the generic directional flow of billiards in… (More)
Let X1; X2; : : : ; Xn be a sequence of independent, identically distributed positive integer random variables. We study the asymptotics of the likelihood that the sample maximum is achieved k times… (More)
We consider the question of how approximations satisfying Dirichlet’s theorem spiral around vectors in Rd. We give pointwise almost everywhere results (using only the Birkhoff ergodic theorem on the… (More)
We construct a Poincaré section for the horocycle flow on the modular surface SL(2,R)/SL(2,Z), and study the associated first return map, which coincides with a transformation (the BCZ map) defined… (More)
We announce ultrametric analogues of the results of Kleinbock-Margulis for shrinking target properties of semisimple group actions on symmetric spaces. The main applications are S-arithmetic… (More)
We prove analogues of the logarithm laws of Sullivan and Kleinbock-Margulis in the context of unipotent flows. In particular, we obtain results for one-parameter actions on the space of lattices… (More)