Research

PhD thesis (supervisor: Márton Elekes)

Papers

• • Balka, R., Elekes, M., Kiss, V., Nagy, D., Poór, M., Compact sets with large projections and nowhere dense sumset, Nonlinearity, to appear, 2023. 

  • Homa, G., Balka, R., Bernád, J. Z., Károly, M., Csordás, A., Newton's identities and positivity of trace class integral operators,  J. Phys. A: Math. Theor., 56, 145203 (2023). 

  • Balka, R., Elekes, M., Kiss, V., The range of dimensions of microsets, submitted. 

  • Balka, R., Elekes, M., Kiss, V., Stability and measurability of the modified lower dimension, Proc. Amer. Math. Soc., 150 (2022), 3889–3898.

  • Balka, R., Elekes, M., Kiss, V., Poór, M., Singularity of maps of several variables and a problem of Mycielski concerning prevalent homeomorphisms, Adv. Math. 385 (2021).

  • Balka, R., Packing dimension of images and graphs of Gaussian random fields with drift, submitted.

  • Balka, R., Tómács, T., Baum–Katz type theorems with exact threshold, Stochastics 90 (2018), no. 4, 473–503.

  • Angel, O., Balka, R., Máthé, A., Peres, Y., Restrictions of Hölder continuous functions, Trans. Amer. Math. Soc. 370 (2018), no. 6, 4223–4247.

  • Balka, R., Dimensions of fibers of generic continuous maps, Monatsh. Math., 184 (2017), no. 3, 339–378. The final publication is available at link.springer.com.

  • Angel, O., Balka, R., Peres, Y., Increasing subsequences of random walks, Math. Proc. Cambridge Philos. Soc. 163 (2017), no. 1, 173–185.

  • Balka, R., Peres, Y., Uniform dimension results for fractional Brownian motion, J. Fractal Geom. 4 (2017), no. 2, 147–183.

  • Balka, R., Darji, U. B., Elekes, M., Bruckner–Garg-type results with respect to Haar null sets in C[0,1], Proc. Edinb. Math. Soc. (2) 60 (2017), no. 1, 17–30.

  • Balka, R., Dimensions of graphs of prevalent continuous maps, J. Fractal Geom. 3 (2016), no. 4, 407–428.

  • Balka, R., Darji, U. B., Elekes, M., Hausdorff and packing dimension of fibers and graphs of prevalent continuous maps, Adv. Math. 293 (2016), 221–274.

  • Balka, R., Buczolich, Z., Elekes, M., A new fractal dimension: The topological Hausdorff dimension, Adv. Math. 274 (2015), 881–927.

  • Balka, R., Elekes, M., Máthé, A., Answer to a question of Kolmogorov, Proc. Amer. Math. Soc. 143 (2015), no. 5, 2085–2089.

  • Balka, R., Peres, Y., Restrictions of Brownian motion, C. R. Math. Acad. Sci. Paris 352 (2014), no. 12, 1057–1061.

  • Balka, R., Harangi, V., Intersection of continua and rectifiable curves, Proc. Edinb. Math. Soc. (2) 57 (2014), no. 2, 339–345.

  • Balka, R., Inductive topological Hausdorff dimensions and fibers of generic continuous functions, Monatsh. Math. 174 (2014), no. 1, 1–28. The final publication is available at link.springer.com.

  • Balka, R., Metric spaces admitting only trivial weak contractions, Fund. Math. 221 (2013), no. 1, 83–94.

  • Balka, R., Máthé, A., Generalized Hausdorff measure for generic compact sets, Ann. Acad. Sci. Fenn. Math. 38 (2013), 797–804.

  • Balka, R., Farkas, Á., Fraser, J. M., Hyde, J. T., Dimension and measure for generic continuous images, Ann. Acad. Sci. Fenn. Math. 38 (2013), 389–404.

  • Balka, R., Buczolich, Z., Elekes, M., Topological Hausdorff dimension and level sets of generic continuous functions on fractals, Chaos Solitons Fractals 45 (2012), no. 12, 1579–1589.

  • Balka, R., Elekes, M., Continuous horizontally rigid functions of two variables are affine, Aequationes Math. 84 (2012), no. 1-2, 27–39.

  • Balka, R., Duality between measure and category in uncountable locally compact abelian Polish groups, Real Anal. Exchange 36 (2010), no. 2, 245–256.

  • Balka, R., Elekes, M., The structure of continuous rigid functions of two variables, Real Anal. Exchange 35 (2009), no. 1, 139–156.

  • Balka, R., Elekes, M., The structure of rigid functions, J. Math. Anal. Appl. 345 (2008), no. 2, 880–888.