Professor Eugene Lytvynov

Professor, Mathematics

+44 (0) 1792 602156

e.lytvynov@swansea.ac.uk

Office - 341
Third Floor
Computational Foundry
Bay Campus

Available For Postgraduate Supervision

Research Links

https://orcid.org/0000-0001-9685-7727

ResearchGate

Google Scholar

Scopus

About

I am a mathematician working in the fields of infinite dimensional analysis, theory of point processes and random measures, and noncommutative (quantum) probability.

My most recent works have been on infinite dimensional basis-free umbral calculus and non-Abelian anyon quasiparticles.

Areas Of Expertise

Infinite dimensional analysis
Point processes and random measures
Noncommutative probability
Umbral calculus

Publications

Research Highlights

Lytvynov, E. & Othman, N. (n.d.) Quasi-free states on a class of algebras of multicomponent commutation relations. Reviews in Mathematical Physics
https://doi.org/10.1142/s0129055x23500204, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa63565
http://dx.doi.org/10.1142/s0129055x23500204
Schiavo, L. & Lytvynov, E. (2023). A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability, 28(none)
https://doi.org/10.1214/23-ecp528, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa63328
http://dx.doi.org/10.1214/23-ecp528
Alshehri, M. & Lytvynov, E. (2022). Hafnian point processes and quasi-free states on the CCR algebra. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 25(1)
https://doi.org/10.1142/s0219025722500023, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa58782
Finkelshtein, D., Kondratiev, Y., Lytvynov, E., & Oliveira, M. (2022). Stirling operators in spatial combinatorics. Journal of Functional Analysis, 282(2), 109285
https://doi.org/10.1016/j.jfa.2021.109285, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa58358
Daletskii, A., Kalyuzhny, A., Lytvynov, E., Proskurin, D., & Lytvynov, E. (2020). Fock representations of multicomponent (particularly non-Abelian anyon) commutation relations. Reviews in Mathematical Physics, 32(05), 2030004
https://doi.org/10.1142/s0129055x20300046, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa54446
Finkelshtein, D., Kondratiev, Y., Lytvynov, E., Oliveira, M., & Streit, L. (2019). Sheffer homeomorphisms of spaces of entire functions in infinite dimensional analysis. Journal of Mathematical Analysis and Applications, 479(1), 162-184.
https://doi.org/10.1016/j.jmaa.2019.06.021, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa50766
Lytvynov, E. (2019). Representations of the Anyon Commutation Relations. In Geometric Methods in Physics XXXVI-327).
https://doi.org/10.1007/978-3-030-01156-7_33, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa50118
Finkelshtein, D., Kondratiev, Y., Lytvynov, E., & Oliveira, M. (2019). An infinite dimensional umbral calculus. Journal of Functional Analysis, 276(12), 3714-3766.
https://doi.org/10.1016/j.jfa.2019.03.006, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa49896
Litvinov, W. & Lytvynov, E. (2019). Construction of solutions to parabolic and hyperbolic initial–boundary value problems. Applicable Analysis, 99(14), 2381-2413.
https://doi.org/10.1080/00036811.2019.1566528, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa48055
Bożejko, M., da Silva, J., Kuna, T., & Lytvynov, E. (2018). Approximation of a free Poisson process by systems of freely independent particles. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 21(3), 1850020-1-1850020-25.
https://doi.org/10.1142/S0219025718500200, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa43227

All Research

Journal Articles

Alshehri, M. & Lytvynov, E. (2023). Particle-Hole Transformation in the Continuum and Determinantal Point Processes. Communications in Mathematical Physics
https://doi.org/10.1007/s00220-023-04803-9, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa63994
http://dx.doi.org/10.1007/s00220-023-04803-9
Schiavo, L. & Lytvynov, E. (2023). A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability, 28(none)
https://doi.org/10.1214/23-ecp528, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa63328
http://dx.doi.org/10.1214/23-ecp528
Alshehri, M. & Lytvynov, E. (2022). Hafnian point processes and quasi-free states on the CCR algebra. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 25(1)
https://doi.org/10.1142/s0219025722500023, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa58782
Finkelshtein, D., Kondratiev, Y., Lytvynov, E., & Oliveira, M. (2022). Stirling operators in spatial combinatorics. Journal of Functional Analysis, 282(2), 109285
https://doi.org/10.1016/j.jfa.2021.109285, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa58358
Daletskii, A., Kalyuzhny, A., Lytvynov, E., Proskurin, D., & Lytvynov, E. (2020). Fock representations of multicomponent (particularly non-Abelian anyon) commutation relations. Reviews in Mathematical Physics, 32(05), 2030004
https://doi.org/10.1142/s0129055x20300046, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa54446
Finkelshtein, D., Kondratiev, Y., Lytvynov, E., Oliveira, M., & Streit, L. (2019). Sheffer homeomorphisms of spaces of entire functions in infinite dimensional analysis. Journal of Mathematical Analysis and Applications, 479(1), 162-184.
https://doi.org/10.1016/j.jmaa.2019.06.021, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa50766
Finkelshtein, D., Kondratiev, Y., Lytvynov, E., & Oliveira, M. (2019). An infinite dimensional umbral calculus. Journal of Functional Analysis, 276(12), 3714-3766.
https://doi.org/10.1016/j.jfa.2019.03.006, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa49896
Litvinov, W. & Lytvynov, E. (2019). Construction of solutions to parabolic and hyperbolic initial–boundary value problems. Applicable Analysis, 99(14), 2381-2413.
https://doi.org/10.1080/00036811.2019.1566528, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa48055
Ibraheem, H. & Lytvynov, E. (2018). Quasi-invariance of completely random measures. Methods of Functional Analysis and Topology, 24(3), 207-239.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa38956
http://mfat.imath.kiev.ua/article/?id=1083
Bożejko, M., da Silva, J., Kuna, T., & Lytvynov, E. (2018). Approximation of a free Poisson process by systems of freely independent particles. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 21(3), 1850020-1-1850020-25.
https://doi.org/10.1142/S0219025718500200, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa43227
Lytvynov, E. & Rodionova, I. (2018). Meixner class of orthogonal polynomials of a non-commutative monotone Lévy noise. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 21(02), 1850011
https://doi.org/10.1142/S021902571850011X, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa36409
Bożejko, M., Lytvynov, E., & Wysoczański, J. (2017). Fock representations of Q-deformed commutation relations. Journal of Mathematical Physics, 58(7), 073501
https://doi.org/10.1063/1.4991671, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa34436
Ji, U. & Lytvynov, E. (2017). Wick Calculus for Noncommutative White Noise Corresponding to q-Deformed Commutation Relations. Complex Analysis and Operator Theory
https://doi.org/10.1007/s11785-016-0635-3, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa31576
Lytvynov, E. (2017). Gauge-Invariant Quasi-Free States on the Algebra of the Anyon Commutation Relations. Communications in Mathematical Physics, 351(2), 653-687.
https://doi.org/10.1007/s00220-016-2786-5, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa29639
Conache, D., Kondratiev, Y., & Lytvynov, E. (2016). Equilibrium Diffusion on the Cone of Discrete Radon Measures. Potential Analysis, 44(1), 71-90.
https://doi.org/10.1007/s11118-015-9499-9, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa23989
Kondratiev, Y., Lytvynov, E., & Vershik, A. (2015). Laplace operators on the cone of Radon measures. Journal of Functional Analysis, 269(9), 2947-2976.
https://doi.org/10.1016/j.jfa.2015.06.007, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa23990
Lytvynov, E. (2015). The projection spectral theorem and Jacobi fields. Methods of Functional Analysis and Topology, 21(2), 189-198.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa23988
http://mfat.imath.kiev.ua/article/?id=769
Bozejko, M., Lytvynov, E., & Rodionova, I. (2015). An extended anyon Fock space and noncommutative Meixner-type orthogonal polynomials in infinite dimensions. Russian Mathematical Surveys, 70(5), 857
https://doi.org/10.1070/RM2015v070n05ABEH004965, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa22143
Kondratiev, Y., Kuna, T., & Lytvynov, E. (2015). A moment problem for random discrete measures. Stochastic Processes and their Applications, 125(9), 3541-3569.
https://doi.org/10.1016/j.spa.2015.03.007, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa22142
Das, S. & Lytvynov, E. (2013). A chaotic decomposition for generalized stochastic processes with independent values. Probability and Mathematical Statistics, 33(2), 201-212.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa19101
Lytvynov, E., Olshanski, G., & Lytvynov, E. (2013). Equilibrium Kawasaki dynamics and determinantal point process. Journal of Mathematical Sciences, 190(3), 451-458.
https://doi.org/10.1007/s10958-013-1260-6, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa19098
http://link.springer.com/article/10.1007/s10958-013-1260-6
Lytvynov, E. (2013). Determinantal point processes with $J$-Hermitian correlation kernels. The Annals of Probability, 41(4), 2513-2543.
https://doi.org/10.1214/12-AOP795, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13889
Lytvynov, E. & Olshanski, G. (2013). Equilibrium Kawasaki dynamics and determinantal point processes. Journal of Mathematical Sciences (New York)
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13890
Bożejko, M., Lytvynov, E., & Wysoczański, J. (2012). Noncommutative Lévy Processes for Generalized (Particularly Anyon) Statistics. Communications in Mathematical Physics, 313(2), 535-569.
https://doi.org/10.1007/s00220-012-1437-8, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7544
Guanhua, L. & Lytvynov, E. (2011). A note on equilibrium Glauber and Kawasaki dynamics for permanental point processes. Methods Funct. Anal. Topology, 17, 29-46.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8096
Finkelshtein, D., Kondratiev, Y., Kutoviy, O., & Lytvynov, E. (2011). Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit. Journal of Mathematical Physics, 52(11), 113301
https://doi.org/10.1063/1.3657345, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7543
http://dx.doi.org/10.1063/1.3657345
Finkelshtein, D., Kondratiev, Y., Kutoviy, O., & Lytvynov, E. (2011). Binary jumps in continuum. I. Equilibrium processes and their scaling limits. Journal of Mathematical Physics, 52(6), 063304
https://doi.org/10.1063/1.3601118, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7542
http://dx.doi.org/10.1063/1.3601118
Bożejko, M. & Lytvynov, E. (2010). Meixner Class of Non-commutative Generalized Stochastic Processes with Freely Independent Values II. The Generating Function. Communications in Mathematical Physics, 302(2), 425-451.
https://doi.org/10.1007/s00220-010-1134-4, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1075
Bożejko, M. & Lytvynov, E. (2009). Meixner Class of Non-Commutative Generalized Stochastic Processes with Freely Independent Values I. A Characterization. Communications in Mathematical Physics, 292(1), 99-129.
https://doi.org/10.1007/s00220-009-0837-x, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1074
Lytvynov, E. & Rodionova, I. (2009). LOWERING AND RAISING OPERATORS FOR THE FREE MEIXNER CLASS OF ORTHOGONAL POLYNOMIALS. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 12(03), 387
https://doi.org/10.1142/S0219025709003720, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1077
Kondratiev, Y., Kutoviy, O., & Lytvynov, E. (2008). Diffusion approximation for equilibrium Kawasaki dynamics in continuum. Stochastic Processes and their Applications, 118(7), 1278-1299.
https://doi.org/10.1016/j.spa.2007.09.001, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1076
Lytvynov, E. & Nataliya, O. (2008). A note on equilibrium Glauber and Kawasaki dynamics for fermion point processes. Methods Funct. Anal. Topol., 14(1), 67-80.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8095
KONDRATIEV, Y., LYTVYNOV, E., & Lytvynov, E. (2005). Glauber dynamics of continuous particle systems. Annales de l'Institut Henri Poincare (B) Probability and Statistics, 41(4), 685-702.
https://doi.org/10.1016/j.anihpb.2004.05.002, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1634
Lytvynov, E. (2003). ORTHOGONAL DECOMPOSITIONS FOR LÉVY PROCESSES WITH AN APPLICATION TO THE GAMMA, PASCAL, AND MEIXNER PROCESSES. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 06(01), 73-102.
https://doi.org/10.1142/S0219025703001031, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1631
Lytvynov, E. (2003). Polynomials of Meixner's type in infinite dimensions—Jacobi fields and orthogonality measures. Journal of Functional Analysis, 200(1), 118
https://doi.org/10.1016/S0022-1236(02)00081-2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1632
Röckner, M., Lytvynov, E., Kondratiev, Y., & Grothaus, M. (2003). Scaling limit of stochastic dynamics in classical continuous systems. The Annals of Probability, 31(3), 1494-1532.
https://doi.org/10.1214/aop/1055425788, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1633
Lytvynov, E. & Othman, N. (n.d.) Quasi-free states on a class of algebras of multicomponent commutation relations. Reviews in Mathematical Physics
https://doi.org/10.1142/s0129055x23500204, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa63565
http://dx.doi.org/10.1142/s0129055x23500204
Finkelshtein, D., Lytvynov, E., Oliveira, M., Kuchling, P., & Kondratiev, Y. (n.d.) Analysis on the cone of discrete Radon measures. Pure and Applied Functional Analysis
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa66108

Book Chapters

Hagedorn, D., Kondratiev, Y., Lytvynov, E., & Vershik, A. (2016). Laplace Operators in Gamma Analysis. Stochastic and Infinite Dimensional Analysis -147).
https://doi.org/10.1007/978-3-319-07245-6_7, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa21356

Conference Contributions

Lytvynov, E. (2019). Representations of the Anyon Commutation Relations. In Geometric Methods in Physics XXXVI-327).
https://doi.org/10.1007/978-3-030-01156-7_33, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa50118

Supervision

Lie structures of the Sheffer group over an infinite-dimensional space. (current)

PhD

Other supervisor: Dr Dmitri Finkelshtein
Mean-Field Stochastic Functional Differential Equations with Jumps (current)

PhD

Other supervisor: Prof Chenggui Yuan
Umbral calculus over a Hilbert space. (current)

PhD

Other supervisor: Dr Dmitri Finkelshtein
Generalised Stirling operators, with Applications (current)

PhD

Other supervisor: Dr Dmitri Finkelshtein
Convergence of Numerical Solutions of Stochastic Differential Delay Equations (current)

PhD

Other supervisor: Prof Feng-Yu Wang

Other supervisor: Prof Chenggui Yuan
Quasi-free states on algebra of multicomponent commutation relations (awarded 2023)

PhD

Other supervisor: Dr Dmitri Finkelshtein

Taught Modules

MA-252 Probability Theory

An introduction to fundamental probabilistic concepts and methods such as probability spaces, expectation and variance of random variables, independence, law of large numbers.
MA-311 Partial Differential Equations

This course provides an introduction to the theory of partial differential equations form an analytical perspective.
MA-359 Financial Mathematics in Continuous Time

This module will introduce students to sections 3, 4 and 6 of the Institute and Faculty of Actuaries CM2 syllabus. This module serves as an introduction to the Black-Scholes model for the continuous-time dynamics of a financial market containing a bank account and several kinds of stocks. This theory is based on stochastic (Itô) calculus for Brownian motion. Special attention is paid to the applications of stochastic calculus to the absence of arbitrage in a financial market and pricing and hedging of the options.
MA-M11 Partial Differential Equations

This course provides an introduction to the theory of partial differential equations form an analytical perspective.
MA-M59 Financial Mathematics in Continuous Time

This module will introduce students to sections 3, 4 and 6 of the Institute and Faculty of Actuaries CM2 syllabus. This module serves as an introduction to the Black-Scholes model for the continuous-time dynamics of a financial market containing a bank account and several kinds of stocks. This theory is based on stochastic (Itô) calculus for Brownian motion. Special attention is paid to the applications of stochastic calculus to the absence of arbitrage in a financial market and pricing and hedging of the options.
MARM02 Stochastic Processes (MRes Thesis)

A research project selected from an area of expertise of a member of staff in the Department of Mathematics. It will enable the students to develop an enquiring, analytical critical and creative approach to problem identification and solution. The project will typically focus on a subject area covered within one of the taught modules in the MRes scheme.

Professor Eugene Lytvynov

Telephone number

Email address

Research Links

About

Areas Of Expertise

Publications

Research Highlights

All Research

Journal Articles

Book Chapters

Conference Contributions

Supervision

Lie structures of the Sheffer group over an infinite-dimensional space. (current)

Mean-Field Stochastic Functional Differential Equations with Jumps (current)

Umbral calculus over a Hilbert space. (current)

Generalised Stirling operators, with Applications (current)

Convergence of Numerical Solutions of Stochastic Differential Delay Equations (current)

Quasi-free states on algebra of multicomponent commutation relations (awarded 2023)

Taught Modules

MA-252 Probability Theory

MA-311 Partial Differential Equations

MA-359 Financial Mathematics in Continuous Time

MA-M11 Partial Differential Equations

MA-M59 Financial Mathematics in Continuous Time

MARM02 Stochastic Processes (MRes Thesis)