Deputy director of the Romanovskiy institute of mathematics, Uzbekistan Academy of sciences.
U.A. Rozikov was born on 20 May 1970 in Bukhara, Uzbekistan. He was graduated the Samarkand State University (1993) with an honour diploma. He was a winner of several Mathematical Olympiads. He got Ph.D (1995) and Doctor of sciences in physics and mathematics (2001) degrees from the Institute of Mathematics, Tashkent.
Prof. Utkir Rozikov is an internationally renowned expert in probability, mathematical physics and analysis, specializing in dynamical systems and statistical mechanics on graphs. He represents the strong Tashkent research school which grew from the Dobsrushin-Minlos-Sinai seminar at Moscow in the 1960-70s.
Rozikov has made significant contributions to the deep analysis of Gibbs states in topical models of statistical mechanics on trees (Ising, Potts, SOS), in particular with random interactions and/or in external field. He has promoted new tools in studying Gibbs measures on graphs, such as group representation theory, information flows, node-weighted random walks, contour methods on trees, and non-linear analysis. Rozikov has also advanced the idea of studying p-adic dynamical systems relevant to multiscale and/or chaotic systems, applied to statistical mechanics on trees and Cayley graphs of non-amenable groups. His more recent interests are focussed on evolution algebras of sex-linked populations, aiming to incorporate thermodynamics in mathematical biology models.
Rozikov is an exceptionally prolific author: since 1995, he has published over 140 papers in top journals including 12(!) papers in the flagship Journal of Statistical Physics (Impact Factor 1.202) and also in Lett. Math. Phys. (1.939), Comm. Math. Phys. (2.086), J. Stat. Mech. Theory Exp. (2.404), J. Math. Anal. Appl. (1.120), etc. In particular, in 2013 he published an extensive review paper (112 pages) in Rev. Math. Phys. (1.329), followed by the authoritative research monograph «Gibbs Measures on Cayley Trees» (World Scientific, 2013). He also published books “Population Dynamics: Algebraic and probabilistic approach” (World Scientific, 2020) and «An introduction to mathematical billiards» (World Scientific, 2019).
Rozikov was a visiting professor and invited researcher at many universities and research centres in France, Germany, Italy, Spain, UK, Switzerland and Turkey.
His awards include: Prize of Japan Embassy; Prize of the Uzbek Academy of Sciences; TWAS Prize for Young Scientists; Medal «O’zbekiston Belgisi» from the Government of Uzbekistan. He held research grants from TWAS, DFG, and NATO, and fellowships awarded by CNR (Italy), CNRS (France), ICTP (Trieste, Italy), CPT & IMéRA (Marseille), etc. He is a frequent invited speaker at workshops and seminars abroad, and he collaborates closely with some leading researchers across Europe (France, Germany, Italy, Spain, UK, Switzerland ).
Currently, Rozikov is working on real and p-adic Gibbs measures for spin systems of statistical mechanics on graphs. Moreover, he is developing the theory of dynamical systems and evolution algebras of population biology.
Rozikov’s list of publications (since 2018):
- Rozikov U.A. Population dynamics: algebraic and probabilistic approach. World Sci. Publ. Singapore. 2020, 460 pp.
- Rozikov U.A. An introduction to mathematical billiards. World Sci. Publ. Singapore. 2019, 224 pp.
- Ibragimov Z., Levenberg N., Rozikov U., Sadullaev A. (Eds). Algebra, Complex Analysis, and Pluripotential Theory. Springer Proceedings in Mathematics and Statistics. 2018, V. 264, Springer Nature Switzerland.
- (IF=1.670) Le Ny A., Liao L., Rozikov U.A. p-adic boundary laws and Markov chains on trees, Letters in Mathematical Physics, 2020. DOI: 10.1007/s11005-020-01316-7.
- (IF=0.873) Rozikov U.A., Sattarov I.A. Dynamical systems of the p-adic (2; 2)-rational functions with two xed points. Results in Mathematics, 2020. V. 75., No 3, Paper No. 100, 37 pp.
- Diyorov A. M., Rozikov U. A. Dynamics of a population with different fitness of genotypes. Uzbek Math. J. 2020, No. 1, p. 31-40.
- (IF=1.019) Rozikov U.A., Usmonov J.B. Dynamics of a population with two equal dominated species. Qualit. Theory Dyn. Syst. 2020. V.19., No. 2, Paper No. 62, 19 pp.
- (IF=1.050) Rozikov U.A., Shoyimardonov S.K. Leslie’s prey-predator model in discrete time. Inter. Jour. Biomath. 2020. 2050053, https://doi.org/10.1142/S1793524520500539
- (IF=0.790) Luna A., Rozikov U.A., Sattarov I.A. p-Adic dynamical systems of (3,1)-rational functions with unique _xed point. p-Adic Numbers, Ultrametric Anal. Appl. 2020. V.12., No. 3, p. 210-230.
- Rozikov U. A., Shoyimardonov S. K. A Model for COVID-19 pandemic and prediction for Uzbekistan. Bulletin Inst. Math. 2020, No.2, 19–21.
- (IF=0.370) Absalamov A.T., Rozikov U.A. The dynamics of gonosomal evolution operators. Jour. Appl. Nonlinear Dynamics. 2020, V.9., No.2, 247-257.
- (IF=0.994) Henning F., Kuelske C., Le Ny A., Rozikov U.A. Gradient Gibbs measures for the SOS model with countable values on a Cayley tree. Electronic Journal of Probability. 2019, V. 24, paper no. 104, 1-23.
- (IF=1.019) Hardin A.J.M., Rozikov U.A. A quasi-strictly non-Volterra quadratic stochastic operator. Qualit. Theory Dyn. Syst. 2019. V.18, No.3, p.1013-1029.
- (IF=2.196) Bogachev L.V., Rozikov U.A. On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field. Jour. Stat. Mech.: Theory and Exper. 2019. 073205, 76 pages.
- (IF=0.973) Casas J.M., Ladra M., Rozikov U.A. Markov processes of cubic stochastic matrices: Quadratic stochastic processes. Linear Algebra Appl. 2019. V. 575, 273-298.
- (IF=2.196) Kissel S., Kulske C., Rozikov U.A., Hard-core and soft-core Widom-Rowlinson models on Cayley trees. Jour. Stat. Mech.: Theory and Exper. 2019. P043204, 22 pages.
- (IF=1.050) Rozikov U.A., Shoyimardonov S.K. On ocean ecosystem discrete time dynamics generated by Volterra operators. Inter. Jour. Biomath. 2019. Vol. 12, No. 2, 1950015, (24 pages).
- (IF=0.790) Rozikov U.A., Sattarov I.A., Yam S. p-adic dynamical systems of the function ax.x2+a . p-Adic Numbers, Ultrametric Anal. Appl. 2019. V.11., No.1, p. 77-87.
- (IF=1.940) Rozikov U.A., Velasco M.V. A discrete-time dynamical system and an evolution algebra of mosquito population. Jour. Math. Biology. 2019. V.78., No. 4, p. 1225-1244.
- (IF=0.481) Omirov B. A., Rozikov U. A., Velasco M. V. A class of nilpotent evolution algebras. Communications in Algebra. 2019, V.47., No. 4, p. 1556-1567.
- Rozikov U.A., Khakimov R.M. An extremality of the translation-invariant Gibbs measure for the HC-model on a Cayley tree. Bulletin Inst. Math. 2019, No.2, 17-22.
- Abdullayev A.U., Rozikov U.A. A review of mathematical methods in the social humanities. Bulletin Inst. Math. 2019, No.1, p. 11-18.
- Castanos O., Jamilov U.U., Rozikov U.A. On Volterra quadratic stochastic operators of a two-sex population on S. Uzbek Math. Jour. 2018, No.3, p.37-50.
- Boxonov Z.S., Rozikov U.A. A dynamical system of temperature-dependent sex linked inheritance. Uzbek Math. Jour. 2018, No.2, p.17-31.
- Rozikov U.A. Holliday junctions for the Potts model of DNA. In book: Ibragimov Z. et.al (Eds). Algebra, Complex Analysis, and Pluripotential Theory. Springer Proceedings in Mathematics and Statistics. 2018, V. 264, p.151-165.
- (IF=0.984) Rozikov U.A., Khakimov R.M., Khaidarov F.Kh. Extremality of translation invariant Gibbs measures for Potts model on Cayley tree. Theor.Math. Phys. 2018, V. 196, No. 1, p. 1043-1058.
- (IF=0.604) Rozikov U. A., Botirov G. I. Non-translation-invariant Gibbs measures for models with uncountable set of spin values on a Cayley tree. Reports Math. Phys. 2018, V.81, No.1, p.105-115.