Rebenko Oleksii
Publications
Books and big surveys:
1. Coefficient function equations of the scattering matrix. (with S.S.Ivanov, D..Ya. Petrina). Moscow, "Nauka", 1979, 269 p.(in Russian).
2. The foundation of modern theory of interacting quantum fields. Kyiv, "Naukova dumka", 2007, 538 p. (in Ukranian)pdf.
3. Theory of Interacting Quantum Fields, Monograph, De Gruyter Studies in Mathematics 39, 2012, 584 p.
4. Mathematical foundation of the modern statistical mechanics. Kyiv, "Naukova dumka", 2024, 315 p. (in Ukranian)
S- matrix in constructive quantum field theory (with S.S.Ivanov and D.Ya. Petrina), in: Sov.J. Particles Nucl. (Engl. Transl.), 1976, vol. 7, issue 3, pp. 254-268.
6. Euclidian field theory and ion-dipole systems of classical statistical mechanics, in: Fizika mnogochastistichnych sistem (Russian) (Physics of many-component systems), "Naukova Dumka", Kiev, 1983, pp.77-108.
7.Cluster-expansion method in Euclidian field theory and classical statistical mechanics, in: Sov.J. Particles Nucl. (Engl. Transl.),1985, vol. 16, issue 3, pp. 239-252.
8. Mathematical foundations of equilibrium classical statistical mechanics of charged particles, in: Russian Mathematical Surveys (English transl. from Uspekhi Mat. Nauk), 1988, vol.43, Nu.3, pp. 65–116.
9. Cell gas model of classical statistical systems. Reviews in Math. Phys.,2013. Vol. 25, No 4, 1330006-1-28.
10. Infinitedimentional analysis and statistical mechanics (with V.A.Boluh) Proc. Inst.Math. NASU, 2014, v.11, No1, pp.258-315.
Selected Papers:
Virial Expansions for Correlation Functions in Canonical Ensemble. {\it Letters in Mathematical Physics} (2023) 113:85, 1-14.
https://doi.org/10.1007/s11005-023-01704-9
The new simplest proof of Ceyley's formula and connections with Kirkwood-Salzburg equations. {\it Ukr. Math. Journ.} 2022, 74, No 10, p. 1441--1444, DOI: 10.37863/umzh.v74i10.7156
On the relationship between some approaches to the solution of Kirkwood-Salsburg equations. {\it Ukrainian Mathematical Journal}, Vol. 73, No. 3, August, 2021, pp. 447--462
A combinatorial identity with applications to forest graphs
{\it Discrete Mathematics,} v. 344, issue 4, 2021, 112270
(with T. Dorlas and B. Savoie)
Correlation of clusters: partially truncated correlation functions and their decay. {\it
Journ. Math.Phys.}, v.61, No 3 (2020), p. 033301-30(with T. Dorlas and B.Savoie)
Property of Mixing of Continuous Classical Systems with Strong Superstable Interactions (with M.V . Tertychnyi)
Ukrainian Mathematical Journal, 2018, 69 (8), 1262-1274.
Approximation by Finite Potentials (with P.V. Malyshev)
Ukrainian Mathematical Journal, 2014, 65 (10), 1490-1497.
An exponential representation for some integrals with respect to Lebesque-Poisson measure (with V.A. Boluh) Method Funct. Anal. and Topology, 2014, v.20,no 2, pp.186-192.
Cell gas model of classical statistical systems. Reviews in Math. Phys.,2013. Vol. 25, No 4, 1330006-1-28.
Про квазінеперервну апроксимацію в класичній статистичній механіці (з С.М. Петренко, М.В. Тертичним ). Укр.мат.жур., 2011, 63, вип. 3, с. 369-384.
Quasilattice Approximation of Statistical Systems with Strong Superstable interactions. Correlation functions (with M. V. Tertychnyi). 50,2009. No 3, p. 033301 pdf.
On stability, superstability and strong superstability of classical systems of statistical mechanics (withM. V. Tertychnyi). Methods Funct. Anal. and Topology, 2008, 14, no. 3, pp. 287- 296 pdf.
Superstable criterion and superstable bounds for in nite range interaction I: two-body potentials (with S.M. Petrenko). Methods Funct. Anal. Topology, 2007, vol. 13, no. 1, pp. 50 - 61.
Gibbs State Uniqueness for Anharmonic Quantum Crystal with a Nonpolynomial Double-well Potential(with V.A. Zagrebnov). Journ. Stat. Mechanics: Theory and Experiment (2006), P09002 (Electronic journal) pdf.
Polymer Expansions for Continuous Classical Systems with Manybody Interaction. Meth. Funct. Anal. and Topology, 2004, 11, no.1, 73-87.
On Diffusion Dynamics for Continuous Systems with singular Superstable Interaction (with Yu.G.Kondratiev and M.Rockner). Journ. Math.Phys., 2004, 45, N 5, 1-22. pdf.
Existence of Gibbs State for Continuous Gas withMany-Body Interaction (with O.V. Kutoviy). Jour. Math. Phys., 2004, 45, No. 3, 22-35.
Euclidean Gibbs states of quantum continuous systems via claster expansions. II. Bose-Fermi Statistics. Meth. of Func. Anal.and Topology, 1999, 5, no. 3, pp.86-100. pdf.
High and Low temperature expansions in the Classical Statistical Mechanics of continuous systems. In: Proceeding of Satellite Coll.Math.results in Stat.Mech.,Marseille, 1999 pdf.
Small mass behaviour of quantum Gibbs states for lattice models with unbounded spins (with S. Albeverio, Yu. G. Kondratiev and R. A.Minlos). Journal Stat.Phys., 1999, 92, no. 5/6, pp.1153-1172.
Peierls argument and long-range order behaviour of quantum lattice systems with unbounded spins (with S. Albeverio and A. Yu. Kondratiev). Journal Stat. Phys., 1998, 92, no. 5/6, p.1137-1152.
A new proof of Ruelle's superstability bounds. Journ. Stat. Phys., 1998, 91, no. 3/4. pp. 815-826.
Euclidean Gibbs states for quantum continuous systems with Boltzmann statistics via cluster expansions (with Yu. G. Kondratiev, E.W. Lytvynov, M. Rockner, G. V. Shchepan'uk). Meth. of Func. Anal.and Topology, 1997, 3, no. 1, 1-27.
The convergence of cluster expansions for continuous systems with manybody interaction (with G. V. Shchepan'uk). Journal Stat. Phys., 1997, vol.88, no. 3/4, pp. 665-689.
Wick culculus on spaces of generalized functions of compound Poisson white noise (with E. W. Lytvynov and G. V. Shchepan'uk). Reports on Math. Phys., 1997, 39, no. 2, P. 219-248.
Cluster expansions of the BrydgesFederbush type for quantum lattice systems (with A. Yu. Kondratiev). Meth. Func. Anal. and Topology, 1996, v. 2, no. 3/4, pp. 59-68.
Some remarks about cluser expansions for unbounded continuous spin systems in quantum statistical mechanics (with A. Yu. Kondratiev). Meth. Func. Anal.and Topology, 1996, vol.2, no. 2.
On the Poisson Integrals Representation in the Classical Statistical Mechanics of Continuous Systems (with R. Gielerak). Journal of Math. Physics, 1996, vol.37, pp. 3354-3374.
Poisson analysis and StatisticalMechanics. Jour. of Condensed Matter Physics, 1996, no. 8, pp. 119-127.
Wick Theorems in Non-Gaussian White Noise Calculus (with E. W. Lytvynov and G. V. Shchepan'uk). Reports in Mathematical Physics, 1996, vol. 37, pp. 217-232.
The Large Derivation Principle and BCSModel (with A. I. Pilyavsky). Jour. of Statistical Physics, 1994, vol. 74, no 5/6, 1321-1323.
Poisson Field Representation in the StatisticalMechanics of Continuous Systems (with R. Gielerak). Jour. Operat. Theory: Advances and Applications, 1994, vol. 70, pp. 219-226.
Poisson Measure Representation and Cluster Expansion in Classical Statistical Mechanics. Commun.in Math. Phys., 1993, vol. 151, pp. 427-435. pdf.
Об обобщённых решениях диффузионной иерархии Боголюбова в термодинамическом пределе. Кластерные разложения (совместно с А.И.Пилявским). Теор. Мат.Физика, 1992, 93, №1, 119-137.
Борелевское суммирование разложений Бриджеса-Федербуша-Майера для многочастичных потенциалов (совместно с П.В.Резниченко), Укр. мат. журн., 1992, 43,№ 5, 648-657.
Математическое описание системы заряженных частиц вблизи поверхности пористой мембраны (совместно с В.В.Горунович), Укр. мат. журн., 1988б 40, № 1, С.114-117.
Дебаевское екранирование в пространственно-неоднородных системах заряженных частиц. Модель сферического диелектрика (совместно с А.И.Пилявским). Теор.Мат.Физ., 1986, 69, № 2.
Дебаевское екранирование в пространственно-неоднородных системах заряженных частиц. II. Доказательство сходимости кластерных разложений (совместно с А.И.Пилявским). Теор.Мат.Физ., 1987, 70, № 2.
Функции распределения ионов и диполей вблизи сферической поверхности. Экранированные потенциалы. ДАН УССР, 1984. сер.А, № 2. 59-62.
О существовании дебаевского экранирования в ионно-дипольных классических системах. ДАН СССР, 1982, 267, №6, стр.1350-1352.
Кластерное разложение для ионно-дипольных систем.
Теор.Мат.Физ., 1982, 53, №3, 429-443.
Проекционно-итеративный метод решения уравнений квантовой теории поля и его связь с теорией перенормировок. Уравнения квантовой теории поля и некорректно поставленные задачи математической физики. Теор.Мат.Физ., 1980, 42, №2, 167-183.
S-матрица в конструктивной теории поля.I (совместно с Д.Я.Петриной и С.С.Ивановым). Теор.Мат.Физ., 1975, 23, № 2, 160-177.
Euclidean Fermi fields and Green functions without momentum cutoff for Yukawa2-field theory.}, Preprint ITP-74-54E, Kiev, 1974.
Уравнения для коэффициентных функций S-матрицы в квантовой теории поля (совместно с Д.Я.Петриной и С.С.Ивановым). Теор.Мат.Физ., 1974, 19, № 1, 37-52.
О сходимости рядов теории возмущений в моделях теории поля, содержащих фермионы(совместно с С.С.Ивановым). Теор.Мат.Физ., 1972, 11, № 2, стр. 190-203.
Об уравнениях для матричных элементов эвклидовой квантовой электродинамики. Теор.Мат.Физ., 1972,11, № 3, стр. 301-317.
1. Coefficient function equations of the scattering matrix. (with S.S.Ivanov, D..Ya. Petrina). Moscow, "Nauka", 1979, 269 p.(in Russian).
2. The foundation of modern theory of interacting quantum fields. Kyiv, "Naukova dumka", 2007, 538 p. (in Ukranian)
3. Theory of Interacting Quantum Fields, Monograph, De Gruyter Studies in Mathematics 39, 2012, 584 p.
4. Mathematical foundation of the modern statistical mechanics. Kyiv, "Naukova dumka", 2024, 315 p. (in Ukranian)
S- matrix in constructive quantum field theory (with S.S.Ivanov and D.Ya. Petrina), in: Sov.J. Particles Nucl. (Engl. Transl.), 1976, vol. 7, issue 3, pp. 254-268.
6. Euclidian field theory and ion-dipole systems of classical statistical mechanics, in: Fizika mnogochastistichnych sistem (Russian) (Physics of many-component systems), "Naukova Dumka", Kiev, 1983, pp.77-108.
7.Cluster-expansion method in Euclidian field theory and classical statistical mechanics, in: Sov.J. Particles Nucl. (Engl. Transl.),1985, vol. 16, issue 3, pp. 239-252.
8. Mathematical foundations of equilibrium classical statistical mechanics of charged particles, in: Russian Mathematical Surveys (English transl. from Uspekhi Mat. Nauk), 1988, vol.43, Nu.3, pp. 65–116.
9. Cell gas model of classical statistical systems. Reviews in Math. Phys.,2013. Vol. 25, No 4, 1330006-1-28.
10. Infinitedimentional analysis and statistical mechanics (with V.A.Boluh) Proc. Inst.Math. NASU, 2014, v.11, No1, pp.258-315.
Selected Papers:
Virial Expansions for Correlation Functions in Canonical Ensemble. {\it Letters in Mathematical Physics} (2023) 113:85, 1-14.
https://doi.org/10.1007/s11005-023-01704-9
The new simplest proof of Ceyley's formula and connections with Kirkwood-Salzburg equations. {\it Ukr. Math. Journ.} 2022, 74, No 10, p. 1441--1444, DOI: 10.37863/umzh.v74i10.7156
On the relationship between some approaches to the solution of Kirkwood-Salsburg equations. {\it Ukrainian Mathematical Journal}, Vol. 73, No. 3, August, 2021, pp. 447--462
A combinatorial identity with applications to forest graphs
{\it Discrete Mathematics,} v. 344, issue 4, 2021, 112270
(with T. Dorlas and B. Savoie)
Correlation of clusters: partially truncated correlation functions and their decay. {\it
Journ. Math.Phys.}, v.61, No 3 (2020), p. 033301-30(with T. Dorlas and B.Savoie)
Property of Mixing of Continuous Classical Systems with Strong Superstable Interactions (with M.V . Tertychnyi)
Ukrainian Mathematical Journal, 2018, 69 (8), 1262-1274.
Approximation by Finite Potentials (with P.V. Malyshev)
Ukrainian Mathematical Journal, 2014, 65 (10), 1490-1497.
An exponential representation for some integrals with respect to Lebesque-Poisson measure (with V.A. Boluh) Method Funct. Anal. and Topology, 2014, v.20,no 2, pp.186-192.
Cell gas model of classical statistical systems. Reviews in Math. Phys.,2013. Vol. 25, No 4, 1330006-1-28.
Про квазінеперервну апроксимацію в класичній статистичній механіці (з С.М. Петренко, М.В. Тертичним ). Укр.мат.жур., 2011, 63, вип. 3, с. 369-384.
Quasilattice Approximation of Statistical Systems with Strong Superstable interactions. Correlation functions (with M. V. Tertychnyi). 50,2009. No 3, p. 033301 pdf.
On stability, superstability and strong superstability of classical systems of statistical mechanics (withM. V. Tertychnyi). Methods Funct. Anal. and Topology, 2008, 14, no. 3, pp. 287- 296 pdf.
Superstable criterion and superstable bounds for in nite range interaction I: two-body potentials (with S.M. Petrenko). Methods Funct. Anal. Topology, 2007, vol. 13, no. 1, pp. 50 - 61.
Gibbs State Uniqueness for Anharmonic Quantum Crystal with a Nonpolynomial Double-well Potential(with V.A. Zagrebnov). Journ. Stat. Mechanics: Theory and Experiment (2006), P09002 (Electronic journal) pdf.
Polymer Expansions for Continuous Classical Systems with Manybody Interaction. Meth. Funct. Anal. and Topology, 2004, 11, no.1, 73-87.
On Diffusion Dynamics for Continuous Systems with singular Superstable Interaction (with Yu.G.Kondratiev and M.Rockner). Journ. Math.Phys., 2004, 45, N 5, 1-22. pdf.
Existence of Gibbs State for Continuous Gas withMany-Body Interaction (with O.V. Kutoviy). Jour. Math. Phys., 2004, 45, No. 3, 22-35.
Euclidean Gibbs states of quantum continuous systems via claster expansions. II. Bose-Fermi Statistics. Meth. of Func. Anal.and Topology, 1999, 5, no. 3, pp.86-100. pdf.
High and Low temperature expansions in the Classical Statistical Mechanics of continuous systems. In: Proceeding of Satellite Coll.Math.results in Stat.Mech.,Marseille, 1999 pdf.
Small mass behaviour of quantum Gibbs states for lattice models with unbounded spins (with S. Albeverio, Yu. G. Kondratiev and R. A.Minlos). Journal Stat.Phys., 1999, 92, no. 5/6, pp.1153-1172.
Peierls argument and long-range order behaviour of quantum lattice systems with unbounded spins (with S. Albeverio and A. Yu. Kondratiev). Journal Stat. Phys., 1998, 92, no. 5/6, p.1137-1152.
A new proof of Ruelle's superstability bounds. Journ. Stat. Phys., 1998, 91, no. 3/4. pp. 815-826.
Euclidean Gibbs states for quantum continuous systems with Boltzmann statistics via cluster expansions (with Yu. G. Kondratiev, E.W. Lytvynov, M. Rockner, G. V. Shchepan'uk). Meth. of Func. Anal.and Topology, 1997, 3, no. 1, 1-27.
The convergence of cluster expansions for continuous systems with manybody interaction (with G. V. Shchepan'uk). Journal Stat. Phys., 1997, vol.88, no. 3/4, pp. 665-689.
Wick culculus on spaces of generalized functions of compound Poisson white noise (with E. W. Lytvynov and G. V. Shchepan'uk). Reports on Math. Phys., 1997, 39, no. 2, P. 219-248.
Cluster expansions of the BrydgesFederbush type for quantum lattice systems (with A. Yu. Kondratiev). Meth. Func. Anal. and Topology, 1996, v. 2, no. 3/4, pp. 59-68.
Some remarks about cluser expansions for unbounded continuous spin systems in quantum statistical mechanics (with A. Yu. Kondratiev). Meth. Func. Anal.and Topology, 1996, vol.2, no. 2.
On the Poisson Integrals Representation in the Classical Statistical Mechanics of Continuous Systems (with R. Gielerak). Journal of Math. Physics, 1996, vol.37, pp. 3354-3374.
Poisson analysis and StatisticalMechanics. Jour. of Condensed Matter Physics, 1996, no. 8, pp. 119-127.
Wick Theorems in Non-Gaussian White Noise Calculus (with E. W. Lytvynov and G. V. Shchepan'uk). Reports in Mathematical Physics, 1996, vol. 37, pp. 217-232.
The Large Derivation Principle and BCSModel (with A. I. Pilyavsky). Jour. of Statistical Physics, 1994, vol. 74, no 5/6, 1321-1323.
Poisson Field Representation in the StatisticalMechanics of Continuous Systems (with R. Gielerak). Jour. Operat. Theory: Advances and Applications, 1994, vol. 70, pp. 219-226.
Poisson Measure Representation and Cluster Expansion in Classical Statistical Mechanics. Commun.in Math. Phys., 1993, vol. 151, pp. 427-435. pdf.
Об обобщённых решениях диффузионной иерархии Боголюбова в термодинамическом пределе. Кластерные разложения (совместно с А.И.Пилявским). Теор. Мат.Физика, 1992, 93, №1, 119-137.
Борелевское суммирование разложений Бриджеса-Федербуша-Майера для многочастичных потенциалов (совместно с П.В.Резниченко), Укр. мат. журн., 1992, 43,№ 5, 648-657.
Математическое описание системы заряженных частиц вблизи поверхности пористой мембраны (совместно с В.В.Горунович), Укр. мат. журн., 1988б 40, № 1, С.114-117.
Дебаевское екранирование в пространственно-неоднородных системах заряженных частиц. Модель сферического диелектрика (совместно с А.И.Пилявским). Теор.Мат.Физ., 1986, 69, № 2.
Дебаевское екранирование в пространственно-неоднородных системах заряженных частиц. II. Доказательство сходимости кластерных разложений (совместно с А.И.Пилявским). Теор.Мат.Физ., 1987, 70, № 2.
Функции распределения ионов и диполей вблизи сферической поверхности. Экранированные потенциалы. ДАН УССР, 1984. сер.А, № 2. 59-62.
О существовании дебаевского экранирования в ионно-дипольных классических системах. ДАН СССР, 1982, 267, №6, стр.1350-1352.
Кластерное разложение для ионно-дипольных систем.
Теор.Мат.Физ., 1982, 53, №3, 429-443.
Проекционно-итеративный метод решения уравнений квантовой теории поля и его связь с теорией перенормировок. Уравнения квантовой теории поля и некорректно поставленные задачи математической физики. Теор.Мат.Физ., 1980, 42, №2, 167-183.
S-матрица в конструктивной теории поля.I (совместно с Д.Я.Петриной и С.С.Ивановым). Теор.Мат.Физ., 1975, 23, № 2, 160-177.
Euclidean Fermi fields and Green functions without momentum cutoff for Yukawa2-field theory.}, Preprint ITP-74-54E, Kiev, 1974.
Уравнения для коэффициентных функций S-матрицы в квантовой теории поля (совместно с Д.Я.Петриной и С.С.Ивановым). Теор.Мат.Физ., 1974, 19, № 1, 37-52.
О сходимости рядов теории возмущений в моделях теории поля, содержащих фермионы(совместно с С.С.Ивановым). Теор.Мат.Физ., 1972, 11, № 2, стр. 190-203.
Об уравнениях для матричных элементов эвклидовой квантовой электродинамики. Теор.Мат.Физ., 1972,11, № 3, стр. 301-317.