Papers on fractal geometry, Bernoulli convolutions, dimension and dynamics.

On the topology of sums in powers of an algebraic number (with N. Sidorov), Preprint, 2009.

The Lebesgue measure of the algebraic difference of two random Cantor sets (with P. Mora and K. Simon) Indagationes Math., to appear. (Revised version, March 29, 2009.)

Quasisymmetric conjugacy between quadratic dynamics and iterated function systems (with K. I. Eroglu and S. Rohde) Ergodic Theory & Dynam. Sys., to appear. (Revised version, July 18, 2009.)

Spacings and pair correlations for finite Bernoulli convolutions (with I. Benjamini) Nonlinearity 22 (2009), 381-393.

Branching Random Walk with Exponentially Decreasing Steps, and Stochastically Self-Similar Measures (with I. Benjamini and O. Gurel- Gurevich) Transactions of the AMS, 361 (2009), no. 3, 1625-1643.

Visibility for self-similar sets of dimension one in the plane (with K. Simon), Real Analysis Exchange 32 (2006/2007), 67-78.

Zeros of {-1,0,1}-power series and connectedness loci for self-affine sets (with P. Shmerkin), Experimental Math. 15 (2006), 499--511.

Absolute continuity for random iterated function systems with overlaps (with Y. Peres and K. Simon), Journal of the London Math. Soc. (2) 74 (2006), 739--756.

Appendix: positive measure self-similar sets without interior (with M. Csornyei, T. Jordan, D. Preiss and M. Pollicott), Ergodic Theory and Dynam. Systems 26 (2006), 755--758.

On the `Mandelbrot set' for pairs of linear maps: asymptotic self-similarity, Nonlinearity 18 (2005), 1927--1943.

The sharp Hausdorff measure condition for length of projections (with Y. Peres), Proc. Amer. Math. Soc. 133 (2005), no. 11, 3371-3379.

The dimension of graph directed attractors with overlaps on the line, with an application to a problem in fractal image recognition (with M. Keane and K. Simon), Fundamenta Math. 180 (2003), 279--292.

Spectra of Bernoulli convolutions as multipliers in $L^p$ on the circle (with Nikita Sidorov), Duke Math. Journal 120 (2003), 353--370.

``Mandelbrot set'' for a pair of linear maps: the local geometry , Analysis in Theory and Applications 20:2 (2004), 149--157.

On the ``Mandelbrot set'' for a pair of linear maps and complex Bernoulli convolutions (with Hui Xu), Nonlinearity 16 1733--1749 (2003)

On the dimension of self-similar sets (with Karoly Simon), Fractals 10, 59-65 (2002)

How likely is Buffon's needle to fall near a planar Cantor set? (with Yuval Peres), Pacific Journal of Math. 204, 473-496 (2002)

L^q densities for measures associated with parabolic IFS with overlaps (with Mariusz Urbanski), Indiana University Math. J. 50, 1845-1866 (2001)

Equivalence of Hausdorff measure and the open set condition for self-conformal sets (with Yuval Peres, Michal Rams, and Karoly Simon), Proc. Amer. Math. Soc. 129, 2689-2699 (2001)

Hausdorff dimension of limit sets for parabolic IFS with overlaps (with Karoly Simon and Mariusz Urbanski), Pacific Journal of Math. 201, 441-478 (2001)

Invariant measures for parabolic IFS with overlaps and random continued fractions (with Karoly Simon and Mariusz Urbanski), Trans. Amer. Math. Soc. 353, 5145-5164 (2001)

Approximation by polynomials with coefficients +/- 1 (with Yuval Peres), Journal of Number Theory 84, 185-197 (2000)

Existence of L^q dimensions and entropy dimension for self-conformal measures (with Yuval Peres), Indiana University Math. Journal 49, 1603--1621 (2000)

Self-similar sets of zero Hausdorff measure and positive packing measure (with Yuval Peres and Karoly Simon), Israel Journal of Math. 117, 353-379 (2000)

Sixty years of Bernoulli convolutions (with Yuval Peres and Wilhelm Schlag), Fractals and Stochastics II, (C. Bandt, S. Graf and M. Zaehle, eds.), Progress in Probability 46, 39-65, Birkhauser, 2000.