Shmerkin, Pablo
Publicaciones (publications)
On the Hausdorff dimension of pinned distance sets. Israel J. Math. 230, no. 2, 949—972, (2019).Hölder coverings of sets of small dimension. Co-author: Eino Rossi. J. Fractal Geom. 6, no. 3, 285—299, (2019).Spatially independent martingales, intersections, and applications. Co-author: Ville Suomala. Mem. Amer. Math. Soc., 251, no. 1195, v+102 pp., (2018).Absolute continuity of
non-homogeneous self-similar measures. Co-authors: Santiago Saglietti and Boris Solomyak. Adv. Math., 335,
60-110, (2018).Squares and their centers.
Co-authors: Tamás Keleti and
Dániel Nagy. J. Anal. Math., 134, no. 2, 643-669, (2018).Self-similar measures:
asymptotic bounds for the dimension and Fourier decay of smooth images. Co-author: Carolina Mosquera. Ann. Acad. Sci. Fenn. Math. 43, no. 2, 823-834, (2018). On distance sets,
box-counting and Ahlfors-regular sets. Discrete Analysis, no. 9, 22p., (2017).Salem Sets with No
Arithmetic Progressions. Int. Math. Res. Not.
IMRN, no. 7, 1929-1941, (2017).L^q dimensions and projections
of random measures. Co-authors: Daniel Galicer, Santiago Saglietti and Alexia Yavicoli.
Nonlinearity 29, no. 9, 2609-2640, (2016). Absolute continuity of
complex Bernoulli convolutions. Co-author: Boris Solomyak. Math. Proc. Cambridge
Philos. Soc., 161, no. 3, 435-453, (2016).Projections of Self-Similar
and Related Fractals: A Survey of Recent Developments. In Fractal Geometry and
Stochastics V. Progress in Probability, Vol. 70. Birkhäuser Basel, (2016). Absolute continuity of
self-similar measures, their projections and convolutions. Co-author: Boris Solomyak. Trans. Amer. Math. Soc., 368, no.
7, 5125-5151, (2016). On the dimensions of a
family of overlapping self-affine carpets. Co-author: Jonathan Fraser. Ergodic Theory Dynam.
Systems, 36, no. 8, 2463-2481, (2016).
Equidistribution from fractal measures. Co-author: Michael Hochman. Invent. Math., 202, no. 1, pp. 427-479, (2015).Sets which are not tube null and intersection properties of random measures. Co-author: Ville Suomala. J. Lond. Math. Soc., (2) 91, no. 2, pp. 405-422, (2015).Dynamics of the scenery flow and geometry of measures. Co-authors: Antti Käenmäki and Tuomas Sahlsten. Proc. Lond. Math. Soc., (3) 110, no. 5, pp. 1248-1280, (2015).Structure of distributions generated by the scenery flow. Co-authors: Antti Käenmäki and Tuomas Sahlsten. J. Lond. Math. Soc., (2) 91, no. 2, pp. 464-494, (2015).Non-conformal Repellers and the Continuity of Pressure for Matrix Cocycles. Co-author: De-Jun Feng. Geom. Funct. Anal., 24, no. 4, pp. 1101-1128, (2014).Self-affine sets and the continuity of subadditive pressure . In Geometry and Analysis of fractals. Springer Proceedings in Mathematics & Statistics, vol. 88, (2014).On the Exceptional Set for Absolute Continuity of Bernoulli Convolutions. Geom. Funct. Anal., 24, no. 3, pp. 946-958, (2014).On packing measures and a theorem of Besicovitch. Co-author: Ignacio Garcia. Proc. Amer. Math. Soc., 142, no. 8, pp. 2661-2669, (2014).Dimension, entropy and the local distribution of measures. Co-authors: Tuomas Sahlsten and Ville Suomala. J. Lond. Math. Soc., (2) 87, no. 1, pp. 247-268, (2013).Local entropy averages and projections of fractal measures. Co-author: Michael Hochman. Ann. of Math., (2) 175, no. 3, pp. 1001-1059, (2012).T he dimension of weakly mean porous measures: a probabilistic approach. Int. Math. Res. Not. IMRN, no. 9, pp. 2010-2033, (2012).Convolutions of Cantor measures without resonance. Co-authors: Fedor Nazarov and Yuval Peres. Israel J. Math., 187, pp. 93-116, (2012).Visible parts of fractal percolation. Co-authors: Ida Arhosalo, Esa Järvenpää, Maarit Järvenpää and Michał Rams. Proc. Edinb. Math. Soc., (2) 55, no. 2, pp. 311-331, (2012).Multifractal structure of Bernoulli convolutions. Co-authors: Thomas Jordan and Boris Solomyak. Math. Proc. Cambridge Philos. Soc., 151, no. 3, pp. 521-539, (2011).Porosity, dimension, and local entropies: a survey. Rev. Un. Mat. Argentina, 52, no. 2, pp. 81-103, (2011).On the dimension of iterated sumsets . Co-author: Jörg Schmeling. Recent developments in fractals and related fields, 55-72, Appl. Numer. Harmon. Anal. Birkhäuser Boston, Inc., Boston, MA, (2010). The Hausdorff dimension of the projections of self-affine carpets. Co-authors: Andrew Ferguson and Thomas Jordan. Fund. Math., 209, no. 3, 193-213, (2010). Overlapping self-affine sets of Kakeya type. Co-author: Antti Käenmäki. Ergodic Theory Dynam. Systems, 29, no. 3, pp. 941-965, (2009). Resonance between Cantor sets. Co-author: Yuval Peres. Ergodic Theory Dynam. Systems, 29, no. 1, pp. 201-221, (2009). Zeros of {-1,0,1} power series and connectedness loci for self-affine sets. Co-author: Boris Solomyak. Experiment. Math., 15, no. 4, pp. 499-511, (2006). Overlapping self-affine sets. Indiana Univ. Math. J., 55, no. 4, pp. 1291-1331, (2006). A modified multifractal formalism for a class of self-similar measures with overlap. Asian J. Math., 9, no. 3, pp. 323-348, (2005).