
Prof. Dr. Alexander Iksanov,
Operations Research Department,
Faculty of Computer Science and Cybernetics,
Taras Shevchenko National University of Kyiv,
Kyiv01601, Ukraine.
Education and scientific career:
1995
Faculty of Cybernetics, National Taras Shevchenko University of Kyiv
2000
PhD
2008
Habilitation in Physics and Mathematics (doctor phisykomatematychnyh nauk).
Teaching and other experience:
20022008
Associate professor
20042006
Deputy dean of faculty of cybernetics
since 2009
Professor
since 2014
Head of Operations Research Department
20192021
Head of the project no. 19ÁÔ01501 “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:
Mathematics
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 socalled “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 continuoustime counterparts and proposes new methods of studying their evolution with the help of welldeveloped 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 vptrees.

Modphi 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: ISTEJohn 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, 11641204.
4) A. Gnedin, A. Iksanov. (2020).
On nested infinite occupancy scheme in random environment,
Probability Theory and Related Fields, 177, no. 34, 855890.
5) Z. Kabluchko, A. Marynych, D. Temesvari, C. Thäle. (2019).
Cones generated by random points on halfspheres and convex hulls of Poisson point processes,
Probability Theory and Related Fields, 170, no. 3, 10211061.
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, 45854603.
7) A. Bostan, A. Marynych, K. Raschel. (2019).
On the least common multiple of several random integers,
Journal of Number Theory, 204, 113133.
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, 113.
9) A. Gnedin, A. Iksanov, A. Marynych, M. Moehle. (2018).
The collision spectrum of Lambdacoalescents,
Annals of Applied Probability, 28, no. 6, 38573883.
10) A. Iksanov (2016)
Renewal theory for perturbed random walks and similar processes.
Probability and its Applications, Birkhäuser.
ResearchGate Scopus
Contacts
Homepage: http://do.unicyb.kiev.ua/iksan/
Postal address: Taras Shevchenko National University of Kyiv, Faculty of Computer Science and Cybernetics, Ukraine, Kyiv03680, Glushkov Av. 4d
Email: iksan@univ.kiev.ua
