Surveys and Open Problems - Yuval Peres

1. Determinantal Processes and Independence.  (J. Ben Hough, Manjunath Krishnapur, Yuval Peres and Bálint Virág).  Preprint.
2. Sixty years of Bernoulli convolutions. (Y. Peres, W. Schlag and B. Solomyak). Fractal Geometry and Stochastics II, C. Bandt, S. Graf, and M. Zaehle (editors), Progress in Probability Vol. 46, (2000), Birkhauser, pp. 39--65.
3. Problems on self-similar sets and self-affine sets: an update With B. Solomyak. Fractal Geometry and Stochastics II, C. Bandt, S. Graf, and M. Zaehle (editors), Progress in Probability Vol. 46, (2000), Birkh\"{a}user, pp. 95--106.
4. List of Problems suggested in the workshop on "discrete probability and problems from physics", Jerusalem 1996. Problem posers: K. Alexander, N. Alon, I. Benjamini and O. Schramm, C. Borgs and J. Chayes, G. Grimmett, O. H&aumlggstr&oumlm, C. Kenyon, R. Kenyon, H. Kesten, N. Linial, R. Lyons, R. Pemantle, Y. Peres, D. Randall, L. Schulman, J. Steif, O. Zeitouni, Y. Zhang and U. Zwick.
5. The variational principle for Hausdorff dimension: A survey , (With D. Gatzouras). London Math. Soc. Lecture Note Series no. 228, pp. 113--126, edited by M. Pollicott and K. Schmidt (1996), Cambridge University Press.
   Given an expanding self-map f of a compact manifold it is generally accepted that the measure with the greatest geometric significance among f-invariant measures is the one equivalent to Lebesgue measure. (The existence of such a measure is known.) If instead we consider an expanding self-map f of a compact set K of zero Lebesgue measure, the closest analogue to such a measure is an f-invariant measure of full Hausdorff dimension. This survey addresses the existence question for such measures, which is mostly open, and describes the known partial results.
6. Remarks on intersection-equivalence and capacity-equivalence. Ann. Inst. Henri Poincare (Physique theorique) 64 (1996) 339--347.
7. Unsolved problems concerning random walks on trees. (With R. Lyons and R. Pemantle.) In the Proceedings of the June 1994 IMA workshop ``classical and Modern Branching Processes'' (1996), K. B. Athreya and P. Jagers (editors), Springer-Verlag.

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