Mathematical Sciences

Department staff

Dr József Lörinczi

Photo of Dr József Lörinczi

Senior Lecturer

  • 1995: PhD at the University of Groningen, the Netherlands.
  • 1997: Postdoctoral position, University of Leuven
  • 1998: Postdoctoral position, Ludwig-Maximilian University, Munich
  • 1998 - 2008: Researcher and temporary lecturer, Technical University Munich
  • 2008 - present: Senior Lecturer at Loughborough University
  • 1990 & 2008: Visiting fellow, IHES, Bures-sur-Yvette
  • 2000: Visiting fellow, Fields Institute, Toronto
  • 2006: Project Leader of Thematic Programme, Wolfgang Pauli Institute, Vienna

Functional integration (Feynman-Kac-type formulae) for continuous and jump random processes

  • Spectral properties of non-local operators
  • Gibbs measures for discrete and continuous stochastic models
  • Applications in rigorous quantum mechanics and quantum field theory
  • Earlier on: stochastic geometry on lattices and in continuum; positive functionals on C* and von Neumann operator algebras

Selected recent publications:

Monograph

Feynman-Kac-Type Theorems and Gibbs Measures on Path Space. With Applications to Rigorous Quantum Field Theory, Studies in Mathematics 34, Walter de Gruyter, Berlin-New York, 2011, 520pp (2nd edition due in 2015)

Research journal papers

(with K. Kaleta) Pointwise estimates of the eigenfunctions and intrinsic ultracontractivity-type properties of Feynman-Kac semigroups for a class of Lévy processes, to appear in Ann. Probab.

(with F. Hiroshima) Lieb-Thirring bound for Schrödinger operators with Bernstein functions of the Laplacian, Commun. Stoch. Anal. 6, 589-602, 2012

(with F. Hiroshima, T. Ichinose) Probabilistic representation and fall-off of bound states of relativistic Schrödinger operators with spin 1/2, Publ. RIMS 49, 189-214, 2013

(with F. Hiroshima, T. Takaesu) A probabilistic representation of the ground state expectation of fractional powers of the boson number operator, J. Math. Anal. Appl. 395, 437-447 (2012)

(with J. Malecki) Spectral properties of the massless relativistic harmonic oscillator, J. Diff. Equations 253, 2846-2871 (2012)

(with K. Kaleta) Fractional-processes and Gibbs measures, Stoch. Proc. Appl. 122, 3580-3617 (2012)

(with F. Hiroshima, T. Ichinose) Path integral representation for Schrödinger operators with Bernstein functions of the Laplacian, Rev. Math. Phys. 24, 1250013 (2012)

(with M. Gubinelli) Gibbs measures on Brownian currents, Commun. Pure Appl. Math. 62, 1-56 (2009)

(with F. Hiroshima) Functional integral representation of the Pauli-Fierz model with spin 1/2, J. Funct. Anal. 254, 2127-2185 (2008)

  • Project leader of Gibbs measures on paths with jump discontinuities under a pair interaction potential, IHES (2014)
  • Member of Sientific Committee of workshop Fractional Calculus, Probability and Non-local Operators: Applications and Recent Developments, BCAM, Bilbao (2013)
  • Organizer of research-in-peace workshop Lieb-Thirring-Type Bounds for Perturbations of Feller Processes, Institut Mittag-Leffler, Stockholm (2013)
  • Co-organizer of Non-Local Operators: Analysis, Probability, Geometry and Applications, ZiF Bielefeld (2012)
  • Project leader of IUC for Processes with Exponentially Localized Lévy Measure, IHES (2012)
  • Organizer of Research-in-Group Workshop Functional Integration Methods for Non-Local Operators, ICMS Edinburgh (2011)
  • Invited organizer of session Subordinate Brownian Motion and Non-Local Generators, 34th International Conference on Stochastic Processes and Applications, Osaka (2010)
  • Project leader of Fractional Schrödinger Operators, IHES (2010)
  • Project leader of Bernstein Functions of the Laplacian, IHES (2009)
  • Project leader of Higher Spin Algebras and Lévy Measures, IHES (2008)
  • Project leader and organizer of international one-year thematic programme At the Interface of PDE, Self-Adjoint Operators and Stochastics: Models with Exclusion, WPI Vienna (2006)
  • Organizer of workshops Feynman-Kac Formulas and their Applications and Heat Kernels on Manifolds and Isoperimetric Inequalities, WPI (2006)
  • International research grant holder (FOM, the Netherlands; DFG, Germany; START, Austria; JSPS, Japan)

Lecturing

  • MAA270 Introductory Probability and Statistics
  • MAC176 Graph Theory
  • MAP204 Stochastic Calculus and Theory of Stochastic Pricing

Supervision

  • Post-doctoral visitors: Toshimitsu Takaesu (Kyushu University, 2011/12), Soumaya Gheryani (Tunis University, 2011, 2013)
  • Current PhD students: Samuel Durugo, Paul Jones (co-supervised), Xue Li
  • MSc students in stochastic analysis/financial mathematics (2008 --), one BSc student in discrete probability (2009), one industrial placement student (2012), one Nuffield Foundation research student (2011); several research students at European universities (before 2008)