Pieter Allaart

Previous Scheduled Teaching

Published Intellectual Contributions

Journal Article

• Allaart, P.C., Kong, D. (2023). Critical values for the beta-transformation with a hole at 0. Ergodic Theory and Dynamical Systems. 43 (6) 1785-1828.
• Allaart, P.C., Jackson, S.C., Jones, R.T., Lambert, D. (2023). On the existence of numbers with matching continued fraction and decimal expansions. Monatshefte für Mathematik. 202 (1) 1-30.
• Allaart, P., Jones, R.T. (2023). Box-counting dimension and differentiability of box-like statistically self-affine functions. Journal of Mathematical Analysis and Applications. 521 (2) Article 126909, 20 pages.
• Allaart, P.C., Kong, D. (2022). Density spectrum of Cantor measure. Nonlinearity. 35 (12) 6453–6484.
• Allaart, P.C., Kong, D. (2021). Relative bifurcation sets and the local dimension of univoque bases. Ergodic Theory and Dynamical Systems. 41 (8) 2241-2273.
• Allaart, P.C., Kong, D. (2021). On the smallest base in which a number has a unique expansion. Transactions of the American Mathematical Society. 374 (9) 6201-6249.
• Norouzi Kandalan, R., Allaart, P.C., Namuduri, K. (2020). Mobility Accelerates Consensus-Building in Sensor Networks.. IEEE Sensors Letters. 4 (12) 1-4.
• Allaart, P.C. (2020). The pointwise Holder spectrum of general self-affine functions on an interval.. Journal of Mathematical Analysis and Applications. 488 (2) Article 124096, 35 pages. Elsevier.
• Allaart, P., Allen, A. (2019). A random walk version of Robbins' problem: small horizon. Mathematica Applicanda. 47 (2) 293-312.
• Allaart, P. (2019). An algebraic approach to entropy plateaus in non-integer base expansions. Discrete and Continuous Dynamical Systems. 39 (11) 6507-6522.
• Allaart, P., Kong, D. (2019). On the continuity of the Hausdorff dimension of the univoque set. Advances in Mathematics. 354 24 pages.
• Allaart, P., Kong, D., Baker, S. (2019). Bifurcation sets arising from non-integer base expansions. Journal of Fractal Geometry. 6 (4) 301-341.
• Allaart, P. (2018). Differentiability and Holder spectra of a class of self-affine functions. Advances in Mathematics. 328 1-39.
• Allaart, P. (2017). Differentiability of a two-parameter family of self-affine functions. Journal of Mathematical Analysis and Applications. 450 954-968.
• Allaart, P. (2017). On univoque and strongly univoque sets. Advances in Mathematics. 308 575-598.
• Allaart, P., Islas, J.A. (2016). A sharp lower bound for choosing the maximum of an independent sequence. Journal of Applied Probability. 53 (4) 1041-1051.
• Allaart, P. (2016). The infinite derivatives of Okamoto's function: an application of beta-expansions. Journal of Fractal Geometry. 3 (1) 1-31.
• P. Allaart. (2014). Correction and strengthening of ``How large are the level sets of the Takagi function?".
• P. Allaart. (2014). Digital sum inequalities and approximate convexity of Takagi-type functions.
• P. Allaart. (2014). Hausdorff dimension of level sets of generalized Takagi functions.
• Allaart, P. (2014). On the level sets of the Takagi-van der Waerden functions.
• P. Allaart. (2013). Level sets of signed Takagi functions. Acta Mathematica Hungarica.
• Allaart, P. (2012). How large are the level sets of the Takagi function?.
• Allaart, P. (2012). Predicting the supremum: optimality of "stop at once or not at all".
• Allaart, P. (2012). The finite cardinalities of level sets of the Takagi function.
• with K. Kawamura. (2012). The Takagi function: a survey.
• Allaart, P. (2011). An inequality for sums of binary digits, with application to Takagi functions http://arxiv.org/abs/1009.1308 Related Links: http://arxiv.org/abs/1009.1308.
• P. Allaart and K. Kawamura. (2011). Takagi function: Survey. Denton,
• Allaart, P. (2010). A general `bang-bang' principle for predicting the maximum of a random walk..
• Allaart, P. (2010). How to stop near the top in a random walk.
• Allaart, P. (2010). Optimal stopping rules for American and Russian options in a correlated random walk model..
• with K. Kawamura. (2010). The improper infinite derivatives of Takagi's nowhere-differentiable function.
• Allaart, P. (2009). A sharp ratio inequality for optimal stopping when only relative record times are observed.
• with R. D. Mauldin. (2009). Injectivity of the Dubins-Freedman construction of random distributions.
• Allaart, P. (2009). On a flexible class of continuous functions with uniform local structure.
• Allaart, P. (2008). Distribution of the extrema of random Takagi functions.
• with M. Monticino. (2008). Optimal buy/sell strategies for directionally reinforced processes..
• with K. Kawamura. (2007). Dimensions of the coordinate functions of space-filling curves.
• Allaart, P. (2007). Prophet inequalities for i.i.d. random variables with random arrival times.
• with K. Kawamura. (2006). Extreme values of some continuous, nowhere differentiable functions.
• Allaart, P. (2006). Prophet regions for discounted, uniformly bounded random variables.
• with K. Kawamura. (2005). On the coordinate functions of L´evy's dragon curve.
• Allaart, P. (2005). Prophet regions for independent [0, 1]-valued random variables with random dis- counting.
• Allaart, P. (2004). An application of prophet regions to optimal stopping with a random number of observations.
• Allaart, P. (2004). Optimal stopping rules for correlated random walks with a discount.
• Allaart, P. (2004). Stopping the maximum of a correlated random walk, with cost for observation.
• Allaart, P. (2003). Moments of the mean of Dubins-Freedman random probability distributions.
• with M. Monticino. (2003). Pseudo-prophet inequalities in average-optimal stopping.
• with M. Monticino. (2001). Optimal stopping rules for directionally reinforced processes.
• Allaart, P. (2000). Inequalities relating maximal moments to other measures of dispersion.
• Allaart, P. (1999). A sharp non-convexity bound for partition ranges of vector measures with atoms.
• Allaart, P. (1999). Bounds on the non-convexity of ranges of vector measures with atoms.
• Allaart, P. (1998). Minimax risk inequalities for the location-parameter classification problem.
• Allaart, P. (1997). An invariant-sum characterization of Benford's law. Journal of Applied Probability. 34 288-291.

Contracts, Grants and Sponsored Research

Grant - Research

• Allaart, P.C. (Principal), "Non-integer base expansions and multifractal analysis," sponsored by Simons Foundation, Private, $42000 Funded. (2020 - 2025).
• Allaart, P. (Principal), Lazebnik, K.Y. (Co-Principal), Kawamura, K. (Co-Principal), "Conference: Dynamical Systems and Fractal Geometry," sponsored by National Science Foundation, Federal, $32017 Funded. (2024 - 2025).
• Allaart, P. (Principal), "Visitor grant for a 2.5 month research visit to Utrecht University," sponsored by NWO (Dutch National Science Foundation), International, $7000 Funded. (2018 - 2018).
• Allaart, P. (Principal), Schmidt, R. (Principal), "Non-integer base expansions and multifractal analysis," sponsored by Simons Foundation, FOND, Funded. (2020 - 2025).
• Allaart, P.C. (Principal), "Visitor grant for a 2.5 month research visit to Utrecht University," sponsored by NWO (Dutch National Science Foundation), International, Funded. (2018 - 2018).