PUBLICATIONS (by topic)

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Self-similar sets and measures and Bernoulli convolutions

  1. Pablo Shmerkin. On Furstenberg's intersection conjecture, self-similar measures, and the L^q norms of convolutions. Ann. of Math. (2) 189 (2019), no. 2, 319--391. https://arxiv.org/abs/1609.07802 .

  2. Santiago Saglietti, Pablo Shmerkin and Boris Solomyak. Absolute continuity of non-homogeneous self-similar measures. Adv. Math. 335 (2018), 60--110. https://arxiv.org/abs/1709.05092 .

  3. Carolina Mosquera and Pablo Shmerkin. Self-similar measures: asymptotic bounds for the dimension and Fourier decay or smooth images. Ann. Acad. Sci. Fenn. Math. 43 (2018), no. 2, 823--834. https://arxiv.org/abs/1710.06812

  4. Pablo Shmerkin and Boris Solomyak. Absolute continuity of complex Bernoulli convolutions. Math. Proc. Cambridge Philos. Soc. 161 (2016), no. 3, 435--453.  http://arxiv.org/abs/1504.00631 .

  5. Pablo Shmerkin. 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. http://arxiv.org/abs/1501.00875 .

  6. Pablo Shmerkin and Boris Solomyak.  Absolute continuity of self-similar measures, their projections and convolutions. Trans. Amer. Math. Soc. 368(2016), no. 7, 5125--5151. http://arxiv.org/abs/1406.0204 .

  7. Pablo Shmerkin. On the Exceptional Set for Absolute Continuity of Bernoulli Convolutions. Geom. Funct. Anal. 24 (2014), no. 3, 946--958. http://arxiv.org/abs/1303.3992 .

  8. Michael Hochman and Pablo Shmerkin. Local entropy averages and projections of fractal measures. Ann. of Math. (2) 175 (2012), no. 3, 1001--1059. http://arxiv.org/abs/0910.1956 .

  9. Fedor Nazarov, Yuval Peres and Pablo Shmerkin. Convolutions of Cantor measures without resonance. Israel J. Math. 187 (2012), 93--116. http://arxiv.org/abs/0905.3850 .

  10. Thomas Jordan, Pablo Shmerkin and Boris Solomyak. Multifractal structure of Bernoulli convolutions. Math. Proc. Cambridge Philos. Soc. 151 (2011), no. 3, 521--539. http://arxiv.org/abs/1011.1938 .

  11. Yuval Peres and Pablo Shmerkin. Resonance between Cantor sets. Ergodic Theory Dynam. Systems 29 (2009), no. 1, 201--221. http://arxiv.org/abs/0705.2628 .

  12. Pablo Shmerkin. A modified multifractal formalism for a class of self-similar measures with overlap. Asian J. Math. 9 (2005), no. 3, 323--348. http://arxiv.org/abs/math/0408047 .

 

Self-affine sets and the subadditive thermodynamic formalism

  1. Ian D. Morris and Pablo Shmerkin. On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems. Trans. Amer. Math. Soc. 371 (2019), no. 3, 1547--1582. https://arxiv.org/abs/1602.08789 .

  2. Jonathan Fraser and Pablo Shmerkin.  On the dimensions of a family of overlapping self-affine carpets. Ergodic Theory Dynam. Systems 36 (2016), no. 8, 2463--2481. http://arxiv.org/abs/1405.4919 .

  3. De-Jun Feng and Pablo Shmerkin. Non-conformal Repellers and the Continuity of Pressure for Matrix Cocycles. Geom. Funct. Anal. 24 (2014), no. 4, 1101--1128. http://arxiv.org/abs/1311.4241.

  4. Pablo Shmerkin . Self-affine sets and the continuity of subadditive pressure. In Geometry and Analysis of fractals.  Springer Proceedings in Mathematics & Statistics, Vol. 88.  http://arxiv.org/abs/1309.4730 .

  5. Andrew Ferguson, Thomas Jordan, and Pablo Shmerkin. The Hausdorff dimension of the projections of self-affine carpets. Fund. Math. 209 (2010), no. 3, 193--213. http://arxiv.org/abs/0903.2216 .

  6. Antti Käenmäki and Pablo Shmerkin. Overlapping self-affine sets of Kakeya type. Ergodic Theory Dynam. Systems 29 (2009), no. 3, 941--965. http://arxiv.org/abs/0710.0442 .

  7. Pablo Shmerkin and Boris Solomyak. Zeros of {-1,0,1} power series and connectedness loci for self-affine sets. Experiment. Math. 15 (2006), no. 4, 499--511. http://arxiv.org/abs/math/0504545 .

  8. Pablo Shmerkin. Overlapping self-affine sets. Indiana Univ. Math. J. 55 (2006), no. 4, 1291--1331. http://arxiv.org/abs/math/0408203 .

 

Geometric measure theory

  1. Pablo Shmerkin. A nonlinear version of Bourgain's projection theorem. Preprint, https://arxiv.org/abs/2003.01636 .

  2. Pablo Shmerkin and Han Yu. On sets containing a unit distance in every direction. Preprint, https://arxiv.org/abs/1912.01523.

  3. Kornélia Héra, Pablo Shmerkin and Alexia Yavicoli. An improved bound for the dimension of (α,2α)-Furstenberg sets. Preprint, https://arxiv.org/abs/2001.11304 .

  4. Pablo Shmerkin. A nonlinear version of Bourgain's projection theorem. Preprint, https://arxiv.org/abs/2003.01636 .

  5. Kenneth J. Falconer, Jonathan M. Fraser and Pablo Shmerkin. Assouad dimension influences the box and packing dimensions of orthogonal projections. J. Fractal Geom., accepted for publication. https://arxiv.org/abs/1911.04857.

  6. Pablo Shmerkin. Improved bounds for the dimensions of planar distance sets. J. Fractal Geom., accepted for publication.  https://arxiv.org/abs/1811.03379 .

  7. Tamás Keleti and Pablo Shmerkin. New bounds on the dimensions of planar distance sets.  Geom. Funct. Anal. 29 (2019), no. 6, 1886--1948. https://arxiv.org/abs/1801.08745 .

  8. Andrea Olivo and Pablo Shmerkin. Maximal operators for cube skeletons. Ann. Acad. Sci. Fenn. Math., accepted for publication. https://arxiv.org/abs/1807.05280.

  9. Eino Rossi and Pablo Shmerkin. On measures that improve $L^q$ dimension under convolution. Rev. Mat. Iberoam., accepted for publication, 2019. https://arxiv.org/abs/1812.05660.

  10. Eino Rossi and Pablo Shmerkin. Hölder coverings of sets of small dimension.  J. Fractal Geom. 6 (2019), no. 3, 285--299. https://arxiv.org/abs/1702.01130 .

  11. Pablo Shmerkin. On the Hausdorff dimension of pinned distance sets. Israel J. Math. 230 (2019), no. 2, 949--972. https://arxiv.org/abs/1706.00131 .

  12. Pablo Shmerkin and Ville Suomala.  Spatially independent martingales, intersections, and applications. Mem. Amer. Math. Soc. 251 (2018), no. 1195, v+102 pp. http://arxiv.org/abs/1409.6707 .

  13. Tamás Keleti, Dániel Nagy and  Pablo Shmerkin. Squares and their centers. J. Anal. Math. 134 (2018), no. 2, 643-669.  http://arxiv.org/abs/1408.1029 .

  14. Pablo Shmerkin. On distance sets, box-counting and Ahlfors-regular sets. Discrete Analysis, 2017:9, 22p. http://discreteanalysisjournal.com/article/1643-on-distance-sets-box-counting-and-ahlfors-regular-se... ,

  15. Pablo Shmerkin and Ville Suomala. Sets which are not tube null and intersection properties of random measures. J. Lond. Math. Soc. (2) 91 (2015), no. 2, 405--422.  http://arxiv.org/abs/1204.5883v2.

  16. Antti Käenmäki,  Tuomas Sahlsten and Pablo Shmerkin. Dynamics of the scenery flow and geometry of measures. Proc. Lond. Math. Soc. (3) 110 (2015), no. 5, 1248--1280. http://arxiv.org/abs/1401.0231.

  17. Antti Käenmäki,  Tuomas Sahlsten and Pablo Shmerkin. Structure of distributions generated by the scenery flow.  J. Lond. Math. Soc. (2) 91 (2015), no. 2, 464--494. http://arxiv.org/abs/1312.2567 .

  18. Ignacio Garcia and Pablo Shmerkin. On packing measures and a theorem of Besicovitch. Proc. Amer. Math. Soc. 142 (2014), no. 8, 2661--2669. http://arxiv.org/abs/1205.6224 .

  19. Tuomas Sahlsten, Pablo Shmerkin and Ville Suomala. Dimension, entropy and the local distribution of measures. J. Lond. Math. Soc. (2) 87 (2013), no. 1, 247--268. http://arxiv.org/abs/1110.6011 .

  20. Pablo Shmerkin. The dimension of weakly mean porous measures: a probabilistic approach. Int. Math. Res. Not. IMRN 2012, no. 9, 2010--2033. http://arxiv.org/abs/1010.1394 .

  21. Pablo Shmerkin. Porosity, dimension, and local entropies: a survey. Rev. Un. Mat. Argentina 52 (2011), no. 2, 81--103. http://arxiv.org/abs/1110.5682 .

  22. Jörg Schmeling and Pablo Shmerkin. On the dimension of iterated sumsets. Recent developments in fractals and related fields, 55--72, Appl. Numer. Harmon. Anal.,Birkhäuser Boston, Inc., Boston, MA, 2010. http://arxiv.org/abs/0906.1537 .

 

Ergodic Theory

  1. Pablo Shmerkin. On Furstenberg's intersection conjecture, self-similar measures, and the L^q norms of convolutions. Ann. of Math. (2) 189 (2019), no. 2, 319--391. https://arxiv.org/abs/1609.07802 .

  2. Daniel Galicer, Santiago Saglietti, Pablo Shmerkin and Alexia Yavicoli. L^q dimensions and projections of random measures. Nonlinearity 29 (2016), no. 9, 2609--2640. https://arxiv.org/abs/1504.04893 .

  3. Michael Hochman and Pablo Shmerkin. Equidistribution from fractal measures. Invent. Math. 202 (2015), no. 1, 427--479 . http://arxiv.org/abs/1302.5792

  4. Antti Käenmäki,  Tuomas Sahlsten and Pablo Shmerkin. Dynamics of the scenery flow and geometry of measures. Proc. Lond. Math. Soc. (3) 110 (2015), no. 5, 1248--1280. http://arxiv.org/abs/1401.0231.

  5. Antti Käenmäki,  Tuomas Sahlsten and Pablo Shmerkin. Structure of distributions generated by the scenery flow.  J. Lond. Math. Soc. (2) 91 (2015), no. 2, 464--494. http://arxiv.org/abs/1312.2567 .

  6. De-Jun Feng and Pablo Shmerkin. Non-conformal Repellers and the Continuity of Pressure for Matrix Cocycles. Geom. Funct. Anal. 24 (2014), no. 4, 1101--1128. http://arxiv.org/abs/1311.4241.

  7. Pablo Shmerkin . Self-affine sets and the continuity of subadditive pressure. In Geometry and Analysis of fractals.  Springer Proceedings in Mathematics & Statistics, Vol. 88.  http://arxiv.org/abs/1309.4730 .

  8. Michael Hochman and Pablo Shmerkin. Local entropy averages and projections of fractal measures. Ann. of Math. (2) 175 (2012), no. 3, 1001--1059. http://arxiv.org/abs/0910.1956 .

  9. Fedor Nazarov, Yuval Peres and Pablo Shmerkin. Convolutions of Cantor measures without resonance. Israel J. Math. 187 (2012), 93--116. http://arxiv.org/abs/0905.3850 .

  10. Yuval Peres and Pablo Shmerkin. Resonance between Cantor sets. Ergodic Theory Dynam. Systems 29 (2009), no. 1, 201--221. http://arxiv.org/abs/0705.2628 .

 

Additive combinatorics and fractal geometry

  1. Pablo Shmerkin. A nonlinear version of Bourgain's projection theorem. Preprint, https://arxiv.org/abs/2003.01636 .

  2. Jonathan M. Fraser, Pablo Shmerkin and Alexia Yavicoli. Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions. J. Fourier Anal. Appl., accepted for publication. https://arxiv.org/abs/1910.10074 .

  3. Pablo Shmerkin. On the packing dimension of Furstenberg sets. J. Anal. Math., accepted for publication. https://arxiv.org/abs/2006.15569 .

  4. Pablo Shmerkin and Ville Suomala. Patterns in random fractals. Amer. J. Math. 142 (2020), no. 3, 683--749. https://arxiv.org/abs/1703.09553 .

  5. Pablo Shmerkin. On Furstenberg's intersection conjecture, self-similar measures, and the L^q norms of convolutions. Ann. of Math. (2) 189 (2019), no. 2, 319--391. https://arxiv.org/abs/1609.07802 .

  6. Pablo Shmerkin. Salem Sets with No Arithmetic Progressions. Int. Math. Res. Not. IMRN 2017, no. 7, 1929--1941. http://arxiv.org/abs/1510.07596 .

  7. Michael Hochman and Pablo Shmerkin. Local entropy averages and projections of fractal measures. Ann. of Math. (2) 175 (2012), no. 3, 1001--1059. http://arxiv.org/abs/0910.1956 .

  8. Jörg Schmeling and Pablo Shmerkin. On the dimension of iterated sumsets. Recent developments in fractals and related fields, 55--72, Appl. Numer. Harmon. Anal.,Birkhäuser Boston, Inc., Boston, MA, 2010. http://arxiv.org/abs/0906.1537 .

 

Harmonic Analysis

  1. Eino Rossi and Pablo Shmerkin. On measures that improve $L^q$ dimension under convolution. Rev. Mat. Iberoam. 36 (2020), no. 7, 2217--2236.

  2. Andrea Olivo and Pablo Shmerkin. Maximal operators for cube skeletons. Ann. Acad. Sci. Fenn. Math., accepted for publication. https://arxiv.org/abs/1807.05280.

  3. Pablo Shmerkin and Ville Suomala.  Spatially independent martingales, intersections, and applications. Mem. Amer. Math. Soc. 251 (2018), no. 1195, v+102 pp. http://arxiv.org/abs/1409.6707 .

  4. Carolina Mosquera and Pablo Shmerkin. Self-similar measures: asymptotic bounds for the dimension and Fourier decay or smooth images. Ann. Acad. Sci. Fenn. Math. 43 (2018), no. 2, 823--834. https://arxiv.org/abs/1710.06812

  5. Pablo Shmerkin and Ville Suomala. Sets which are not tube null and intersection properties of random measures. J. Lond. Math. Soc. (2) 91 (2015), no. 2, 405--422.  http://arxiv.org/abs/1204.5883v2.

 

Random fractals and applications

  1. Pablo Shmerkin and Ville Suomala. Patterns in random fractals. Amer. J. Math. 142 (2020), no. 3, 683--749. https://arxiv.org/abs/1703.09553 .

  2. Pablo Shmerkin and Ville Suomala.  Spatially independent martingales, intersections, and applications. Mem. Amer. Math. Soc. 251 (2018), no. 1195, v+102 pp. http://arxiv.org/abs/1409.6707 .

  3. Pablo Shmerkin. Salem Sets with No Arithmetic Progressions. Int. Math. Res. Not. IMRN 2017, no. 7, 1929--1941. http://arxiv.org/abs/1510.07596 .

  4. Daniel Galicer, Santiago Saglietti, Pablo Shmerkin and Alexia Yavicoli. L^q dimensions and projections of random measures. Nonlinearity 29 (2016), no. 9, 2609--2640. https://arxiv.org/abs/1504.04893 .

  5. Pablo Shmerkin and Ville Suomala. Sets which are not tube null and intersection properties of random measures. J. Lond. Math. Soc. (2) 91 (2015), no. 2, 405--422.  http://arxiv.org/abs/1204.5883v2.

  6. Ida Arhosalo, Esa Järvenpää, Maarit Järvenpää, Michał Rams and Pablo Shmerkin . Visible parts of fractal percolation. Proc. Edinb. Math. Soc. (2) 55 (2012), no. 2, 311--331. http://arxiv.org/abs/0911.3931 .

 

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