Multivariate Asymptotic Expansions

The aim of this research project is to apply analytic methods to achieve asymptotic expansions of one or more indeterminates. We focus on systems of functional equations, recursively defined generating functions and digital expansions.

The general method employed here is to find generating functions on one or more indeterminates and to deduce asymptotic properties of the coefficients from analytic properties of the power series.

Selected Publications:

  • M. Drmota and B. Gittenberger. On the profile of random trees. Random Structures Algorithms 10/4 (1997), 421-451. [MR], [pdf].
  • M. Drmota. Systems of functional equations. Random Structures Algorithms 10/1-2 (1997), 103-124, Average-case analysis of algorithms (Dagstuhl, 1995). [MR].
  • M. Drmota. On nodes of given degree in random trees. In Probabilistic methods in discrete mathematics (Petrozavodsk, 1996), pages 31-44. VSP, Utrecht, 1997. [MR].
  • M. Drmota and J. Gajdosik. The parity of the sum-of-digits-function of generalized Zeckendorf representations. Fibonacci Quart. 36/1 (1998), 3-19. [MR].
  • M. Drmota and J. Gajdosik. The distribution of the sum-of-digits function. J. Théor. Nombres Bordeaux 10/1 (1998), 17-32. [MR].
  • B. Gittenberger. Convergence of branching processes to the local time of a Bessel process. In Proceedings of the Eighth International Conference ``Random Structures and Algorithms'' (Poznan, 1997), volume 13, pages 423-438, 1998. [MR], [pdf].
  • B. Gittenberger and G. Louchard. The Brownian excursion multi-dimensional local time density. J. Appl. Probab. 36/2 (1999), 350-373. [MR], [pdf].
  • M. Drmota and B. Gittenberger. Strata of random mappings-a combinatorial approach. Stochastic Process. Appl. 82/2 (1999), 157-171. [MR], [pdf].
  • M. Drmota and B. Gittenberger. The distribution of nodes of given degree in random trees. J. Graph Theory 31/3 (1999), 227-253. [MR], [pdf].
  • H. Leinfellner. New results on rarefied sums of the Thue-Morse sequence. In Beiträge zur zahlentheoretischen Analysis, volume 338 of Grazer Math. Ber., pages 9-30. Karl-Franzens-Univ. Graz, Graz, 1999. [MR].
  • B. Gittenberger. On the contour of random trees. SIAM J. Discrete Math. 12/4 (1999), 434-458 (electronic). [MR], [pdf].
  • B. Gittenberger and G. Louchard. On the local time density of the reflecting Brownian bridge. J. Appl. Math. Stochastic Anal. 13/2 (2000), 125-136. [MR], [pdf].
  • M. Drmota. The asymptotic number of leftist trees. Algorithmica 31/3 (2001), 304-317, Mathematical analysis of algorithms. [MR].
  • M. Drmota, D. Gardy, and B. Gittenberger. A unified presentation of some urn models. Algorithmica 29/1-2 (2001), 120-147, Average-case analysis of algorithms (Princeton, NJ, 1998). [MR], [pdf].
  • B. Gittenberger. On the profile of random forests. In Mathematics and computer science, II (Versailles, 2002), Trends Math., pages 279-293. Birkhäuser, Basel, 2002. [MR], [pdf].
  • M. Drmota and B. Gittenberger. The width of Galton-Watson trees conditioned by the size. Discrete Math. Theor. Comput. Sci. 6/2 (2004), 387-400 (electronic). [MR], [pdf].