Alexander Iksanov

Alexander Iksanov

Prof. Dr. Alexander Iksanov,
Operations Research Department,
Faculty of Computer Science and Cybernetics,
Taras Shevchenko National  University of Kyiv,
Kyiv-01601, Ukraine.

Education and scientific career:


Faculty of Cybernetics, National Taras Shevchenko University of Kyiv


Habilitation in Physics and Mathematics (doctor phisyko-matematychnyh nauk).

Teaching and other experience:


Associate professor


Deputy dean of faculty of cybernetics

since 2009


since 2014

Head of Operations Research Department


Head of the project no. 19ÁÔ015-01 “Asymptotic and structural analysis of stochastic models of population dynamics”

Scientific interests in 2019:
1. Random discrete structures (random compositions, coalescents, branching processes etc.).
2. Functional limit theorems.
3. Random processes with immigration (these are renewal shot noise processes with random response functions).
4. Applications of the renewal theory.

Probability, Stochastic Processes

Research Fields:

Previous and Current Research

Mathematical structures, both deterministic and random, may be divided into two classes: discrete and continuous.  In a wide sense, discrete mathematics studies structures with parameters  indexed  by  the  elements  of  discrete  sets  consisting  of  "isolated  members”. Random discrete structures constitute a broad class of probabilistic objects with the characteristics being random variables indexed by space or time parameters varying discretely. The research of our group aims at a special type of discrete random objects having a so-called “regeneration” property. Generally  speaking,  regeneration  means  the  invariance  of  an  exchangeable  or  partially exchangeable random structure, or the family of such structures, under the deletion of a part chosen uniformly at random.  This property provides new insights into the relationship between discrete structures and their continuous-time counterparts and proposes new methods of studying their evolution with the help of well-developed techniques from the theory of stochastic processes. 

Future Projects and Goals

In the near future we intend to continue the aforementioned lines of research as well as start new projects including:

  • Asymptotic theory of locally and globally perturbed random walks.

  • Analysis of random Dirichlet series.

  • Asymptotic results for discounted perpetuities.

  • Various notions of generazlied convexity and analysis of generalized convex hulls of random samples.

  • Asymptotic analysis of random vp-trees.

  • Mod-phi convergence and its consequences in various combinatorial models.

  • Asymptotic analysis of complex systems.

Methodological and Technical Expertise

In particular, our expertise includes:

  • shot noise processes and random processes with immigration;

  • regenerative compositions and partitions;

  • perpetuities and perturbed random walks;

  • functional limit theorems;

  • branching processes; in particular, branching random walks with real and complex parameters, and smoothing transforms;

  • probabilistic number theory;

  • convex stochastic geometry;

  • asymptotic properties of stochastic evolution equations.

Selected Publications

1) A. Marynych, I. Molchanov. (2022).

 Facial structure of strongly convex sets generated by random samples.

 Advances in Mathematics, 395, 108086.

2) Koroliouk D., Samoilenko I. (2021).

Random evolutionary systems: asymptotic properties and large deviations,

London: ISTE-John Wiley & Sons.

3) D. Buraczewski, A. Iksanov, B. Mallein. (2021).

On the derivative martingale in a branching random walk.

Annals of Probability, 49, no. 3, 1164-1204.

4) A. Gnedin, A. Iksanov. (2020).

 On nested infinite occupancy scheme in random environment,

Probability Theory and Related Fields, 177, no. 3-4, 855-890.

5) Z. Kabluchko, A. Marynych, D. Temesvari, C. Thäle. (2019).

 Cones generated by random points on half-spheres and convex hulls of Poisson point processes,

Probability Theory and Related Fields, 170, no. 3, 1021-1061.

6) G. Alsmeyer, Z. Kabluchko, A. Marynych. (2019).

Limit theorems for the least common multiple of a random set of integers,

Transactions of the American Mathematical Society, 372, no. 7, 4585-4603.

7) A. Bostan, A. Marynych, K. Raschel. (2019).

On the least common multiple of several random integers,

Journal of Number Theory, 204, 113-133.

8) A. Iksanov, Z. Kabluchko. (2018).

A functional limit theorem for the profile of random recursive trees,

Electronic Communications in Probability, 23, paper no. 87, 1-13.

9) A. Gnedin, A. Iksanov, A. Marynych, M. Moehle. (2018).

The collision spectrum of Lambda-coalescents,

Annals of Applied Probability, 28, no. 6, 3857-3883.

10) A. Iksanov (2016)

Renewal theory for perturbed random walks and similar processes.

Probability and its Applications, Birkhäuser.

ResearchGate      Scopus



Postal address: Taras Shevchenko National University of Kyiv, Faculty of Computer Science and Cybernetics, Ukraine, Kyiv-03680, Glushkov Av. 4d