PhD thesis (supervisor: Márton Elekes)
Papers
Balka, R., Orgoványi, L., Rutar, A., On the uniformity and size of microsets, submitted.
Balka, R., Keleti, T., New Hausdorff-type dimensions and optimal bound for bilipschitz invariant dimensions, Nonlinearity 38 (2025), 035024.
Balka, R., Csordás, A., Homa, G., Positivity and Entanglement of Polynomial Gaussian Integral Operators; Prog. Theor. Exp. Phys. 2024 no. 10 (2024), 103A01.
Balka, R., Csordás, A., Homa, G., Approximating the eigenvalues of self-adjoint trace class operators, submitted.
Balka, R., Keleti, T., Lipschitz images and dimensions, Adv. Math. 446 (2024), 109669.
Balka, R., Elekes, M., Kiss, V., Nagy, D., Poór, M., Compact sets with large projections and nowhere dense sumset, Nonlinearity 36 (2023), 5190.
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.