Date:
Speaker: Nikolai Leonenko, Cardiff University, UK.
Time : 15:00 - 16.00 CEST (Rome/Paris)
Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy
Zoom link : A link will appear here, one hour before the talk
Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)
* SISSA, International School of Advanced Studies, Italy
** Eastern Mediterranean University, Northern Cyprus
Keywords: Fractional hyperbolic diffusion, spherical random fields, fractional telegraph equation, random data.
Abstract: Spherical random fields are very useful for modelling some phenomena in areas such as earth sciences (like, for example, in geophysics and climatology) and cosmology. In fact, the application of statistical methods in cosmology has become increasingly important due to the many experimental data obtained in recent years, and spherical random fields are of particular interest regarding the analysis of Cosmic Microwave Background (CMB).
As well-known, the CMB is a spatially isotropic radiation field spread throughout the visible universe, originated around 14 billion years ago, and it is the main source of information we have about the evolution of the universe. The CMB radiation can be mathematically modelled as an isotropic spherical random field for which there is a spectral representation by means of spherical harmonics.
Our objective is to study the fundamental solutions to fractional hyperbolic diffusion equation in the time variable using the Caputo derivative, and its properties. The exact solutions of the fractional hyperbolic diffusion equation with random data in terms of series expansions of isotropic in space spherical random fields on the unit sphere are derived, and numerical illustration are presented to illustrate the results.
Some limit theorems for spatio-temporal random fields have been obtained in [1,2].
This is joint results with J.Vaz (UNICAMP, Brazil) and A. Olenko (La Trope University, Melbourne, Australia) [3,4].
Biography: Nikolai Leonenko is a Professor at Cardiff University (UK) since 2006. I joined Cardiff University in 2000. Before he was a full Professor of Kyiv National Taras Shevchenko University, Ukraine and also had some visiting positions in Case Western Reserve University (Clevland, Ohio) and Queensland University of Technology (Brisbane, Australia).
Selected Honors: N. M. Krylov Medal of Academy of Science of Ukraine (1993), the highest annual award for mathematicians in Ukraine.
Google Scholar: Citation 6952 (Google Scholar); h-index 38, i10-index 138; citation in MathSciNet: 1500, 285 published papers, 2 books.
Collaborators: O.E. Barndorff-Nielsen, C.Heyde, M.Taqqu, M.Meershaert, E.Merzbach, N.-R. Shieh, V.Anh, F.Avram, M.D. Ruiz-Medina, I.Podlubny, J.Vaz, I.Nourdin, among the others.
Member of Editorial Board of 5 international journals
In particular NL is Deputy Editor-in-Chief of the journal “Theory Probability and Mathematical Statistics”, AMS, ISSN 1547-7363(online) ISSN 0094-9000(print), and member of EB of “Fractional Calculus and Applied Analysis”, Springer, ISSN 1314-2224 (electronic), ISSN 1311-0454 (print).
Graduate students advised:
I was an advised 19 scientists who received a Ph.D. in Probability Theory and Mathematical Statistics. They work at different Universities of USA, Australia, Italy, Israel, Uzbekistan, Vietnam, Poland, Ukraine, Croatia and Egypt.
Currently I supervise 6 PhD students at Cardiff University.
NL participated in the programme Fractional Differential Equations (FDE2) (January-April 2022) and in the programme Uncertainly Quantification and Modelling of Material Programme (August 2023) in Isaac Newton Institute for Mathematical Sciences, Cambridge. NL participated in the programme "Stochastic systems for anomalous diffusion" in Isaac Newton Institute for Mathematical Sciences, 2024, Cambridge.
https://profiles.cardiff.ac.uk/staff/leonenkon
Bibliography
[1] Leonenko, N., Maini, L., Nourdin, I. and Pistolato, F. (2024) Limit theorems for p-domain functionals of stationary Gaussian fields, Electronic Journal of Probability, 29,1-33
[2] Leonenko, N. and Ruiz-Medina, M.D. (2025) High-Level Moving Excursions for Spatiotemporal Gaussian Random Fields with Long Range Dependence, Journal of Statistical Physics, 192, N2, Paper No. 19, 29pp
[3] Leonenko, N. and Vaz, J. (2020) Spectral analysis of fractional hyperbolic diffusion equations with random data, Journal of Statistical Physics, 179,155-175
[4] Leonenko, N., Olenko, A. and Vaz, J. (2024) On fractional spherically restricted hyperbolic diffusion random field, Communications in Nonlinear Science and Numerical Simulation, 131,107866
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