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Publications for Jozsef Lorinczi Gheryan, S, Hiroshima, F, Lorinczi, J, Majid, A, Ouerdiane, H Functional central limit theorems and $P(phi)_{1}$-processes for the classical and relativistic Nelson models, We construct $P(phi)_1$-processes indexed by the full time-line, separately derived from the functional integral representations of the classical Nelson model and relativistic Nelson model in quantum field theory. Associated with these processes we define a martingale which, under proper scaling, allows to obtain a central limit theorem for additive functionals of the two processes. We show a number of examples by choosing specific functionals related to particle-field operators.. Kaleta, K and Lőrinczi, J (2017) Fall-off of eigenfunctions for non-local Schrödinger operators with decaying potentials, Potential Analysis, 46(4), pp.647-688, ISSN: 1572929X. DOI: 10.1007/s11118-016-9597-3. Lorinczi, J and Sasaki, I (2017) Embedded Eigenvalues and Neumann-Wigner Potentials for Relativistic Schroedinger Operators, Journal of Functional Analysis, ISSN: 0022-1236. DOI: 10.1016/j.jfa.2017.03.012. Lorinczi, J, Kaleta, K, Kwasnicki, M, (Accepted for publication) Contractivity and ground state domination properties for non-local Schrödinger operators, Journal of Spectral Theory, ISSN: 1664-039X. Hiroshima, F, Ichinose, T, Lorinczi, J (2017) Kato's Inequality for Magnetic Relativistic Schrödinger Operators, Publications of the Research Institute for Mathematical Sciences, 53(1), pp.79-117, ISSN: 0454-7845. DOI: 10.4171/PRIMS/53-1-3. Kaleta, K and Lorinczi, J (2016) Transition in the decay rates of stationary distributions of Lévy motion in an energy landscape, Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 93, pp.022135-022142, ISSN: 1063-651X. DOI: 10.1103/PhysRevE.93.022135. Lorinczi, J, Kaleta, K, Durugo, SO (2015) Spectral and Analytic Properties of NonLocal Schrödinger Operators and Related Jump Processes, Communications in Applied and Industrial Mathematics, 6(2), ISSN: 2038-0909. DOI: 10.1685/journal.caim.534. Hiroshima, F, Lörinczi, J, Rozikov, U (2015) Periodic Solutions of Generalized Schrödinger Equations on Cayley Trees, Communications on Stochastic Analysis, 9(2), pp.283-296, Full text: https://www.math.lsu.edu/cosa/contents.htm . Lorinczi, J and Kaleta, K (2015) Pointwise eigenfunction estimates and intrinsic ultracontractivity-type properties of Feynman–Kac semigroups for a class of Lévy processes, Annals of Probability, 43(3), pp.1350-1398, ISSN: 0091-1798. DOI: 10.1214/13-AOP897. Gubinelli, M, Hiroshima, F, Lorinczi, J (2014) Ultraviolet renormalization of the Nelson Hamiltonian through functional integration, Journal of Functional Analysis, 267(9), pp.3125-3153, ISSN: 0022-1236. DOI: 10.1016/j.jfa.2014.08.002. Lorinczi, J and Hiroshima, F (2014) The spectrum of non-local discrete Schrödinger operators with a δ-potential, Pacific Journal of Mathematics for Industry, 6(7), pp.1-6, DOI: 10.1186/s40736-014-0007-8. Hirokawa, M, Hiroshima, F, Lőrinczi, J (2014) Spin-boson model through a Poissondriven stochastic process, Mathematische Zeitschrift, 277(3-4), pp.1165-1198, ISSN: 0025-5874. DOI: 10.1007/s00209-014-1299-1. Hiroshima, F, Ichinose, T, Lorinczi, J (2013) Probabilistic representation and fall-off of bound states of relativistic Schrödinger operators with spin 1/2, Publications of the Research Institute for Mathematical Sciences, 49(1), pp.189-214, ISSN: 0034-5318. DOI: 10.4171/PRIMS/102. Kaleta, K and Lorinczi, J (2012) Fractional P ( φ) 1-processes and Gibbs measures, Stochastic Processes and their Applications, 122(10), pp.3580-3617, ISSN: 0304-4149. DOI: 10.1016/j.spa.2012.06.001. Hiroshima, F, Ichinose, T, Lorinczi, J (2012) Path integral representation for Schrödinger operators with Bernstein functions of the Laplacian, Reviews in Mathematical Physics: a journal for survey and expository articles in the field of mathematical physics, 24, pp.1250013-1250013, ISSN: 1793-6659. DOI: 10.1142/S0129055X12500134. Lorinczi, J (2012) Lieb-Thirring bound for Schrödinger operators with Bernstein functions of the Laplacian, Communications on Stochastic Analysis, 6(4), pp.589-602, Full text: https://www.math.lsu.edu/cosa/contents.htm . Hiroshima, F, Lorinczi, J, Takaesu, T (2012) A probabilistic representation of the ground state expectation of fractional powers of the boson number operator, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 395(2), pp.437-447, ISSN: 0022-247X. DOI: 10.1016/j.jmaa.2012.04.076. Lorinczi, J and Malecki, J (2012) Spectral properties of the massless relativistic harmonic oscillator, JOURNAL OF DIFFERENTIAL EQUATIONS, 253(10), pp.28462871, ISSN: 0022-0396. DOI: 10.1016/j.jde.2012.07.010. Lorinczi, J (2011) Exponential Integrability and DLR Consistence of Some Rough Functionals. In Dalang, RC, Dozzi, M, Russo, F (ed) 6th Seminar on Stochastic Analysis, Random Fields and Applications, SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS VI, Ctr Stefano Franscini, Ascona, SWITZERLAND, pp.191-208, ISBN: 978-3-0348-0020-4. Lorinczi, J, Hiroshima, F, Betz, V (2011) Feynman-Kac-Type Theorems and Gibbs Measures on Path Space. With Applications to Rigorous Quantum Field Theory, Studies in Mathematics 34, Walter de Gruyter, Walter de Gruyter, ISBN: 978-3-11-020148-2. Full text: http://www.degruyter.com/ . Kaleta, K and Lorinczi, J (2010) Analytic properties of fractional Schrodinger semigroups and Gibbs measures for stable processes, preprint 2010. Lorinczi, J (2009) Exponential integrability of some rough functionals. In Proc. Sixth Seminar on Stochastic Analysis, tba, Ascona 2008. Gubinelli, M and Lorinczi, J (2009) Gibbs measures on Brownian currents, Commun. Pure Appl. Math, 62, pp.1-56, DOI: 10.1002/cpa.20260. Gubinelli, M and Lorinczi, J (2009) Ultraviolet renormalization of Nelson's model through functional integration, preprint 2009, pp.1250013-1250013. Hiroshima, F and Lorinczi, J (2008) Functional integral representation of the Pauli-Fierz model with spin 1/2, J. Funct. Anal, 254, pp.2127-2185, DOI: 10.1016/j.jfa.2008.01.002. Hiroshima, F and Lorinczi, J (2008) Erratum to "Functional integral representation of the Pauli-Fierz model with spin 1/2" [J. Funct. Anal. 254 (2008) 2127-2185] (DOI:10.1016/j.jfa.2008.01.002), Journal of Functional Analysis, 254(11), p.2947, ISSN: 0022-1236. DOI: 10.1016/j.jfa.2008.03.009. Lorinczi, J (2008) Rigorous functional integration with applications to QFT. In Janke, W and eds, AP (ed) World Scientific, Path Integrals - New Trends and Perspectives, tba, pp.2127-2185. Lorinczi, J (2007) Fejezetek a matematikai fizikabol, Selected Chapters in Mathematical Physics. Lorinczi, J and Mauser, NJ (2006) A stochastic approach to the bipolaron model, RIMS Kyoto Kokyuroku, 1482, pp.1-10. Georgii, HO, Lorinczi, J, Lukkarinen, J (2005) The continuum Potts model at the disorder-order transition - a study by cluster dynamics, JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, ARTN P06011, ISSN: 1742-5468. DOI: 10.1088/1742-5468/2005/06/P06011. Betz, V, Lorinczi, J, Spohn, H (2005) Gibbs measure for Brownian paths: Theory and Applications, in Interacting Stochastic Systems, J.D. Deuschel and A. Greven (eds). Georgii, HO, Lorinczi, J, Lukkarinen, J (2005) The continuum Potts model at the disorder-order transition - A study by cluster dynamics, Journal of Statistical Mechanics: Theory and Experiment, (6), pp.191-215, ISSN: 1742-5468. DOI: 10.1088/17425468/2005/06/P06011. Betz, V, Lorinczi, J, Spohn, H (2004) Gibbs measures on Brownian paths: Theory and applications, We review our investigations on Gibbs measures relative to Brownian motion, in particular the existence of such measures and their path properties, uniqueness, resp. non-uniqueness. For the case when the energy only depends on increments, we present a functional central limit theorem. We also explain connections with other work and state open problems of interest.. Lorinczi, J (2004) The ground state in Nelson's model with or without infrared cutoff. In Albeverio, S, Ma, ZH, eds, MR (ed) World Scientific Press, Recent Developments in Stochastic Analysis and Related Topics, tba, pp.309-329. Lorinczi, J and Betz, V (2003) Uniqueness of Gibbs measures relative to Brownian motion, Ann Henri Poincare, 39, pp.877-889, DOI: 10.1016/S0246-0203(03)00021-9. Betz, V and Lorinczi, J (2003) Uniqueness of Gibbs measures relative to Brownian motion, Ann. I.H. Poincare, 39, pp.877-889. Betz, V, Hiroshima, F, Lorinczi, J, Minlos, RA, Spohn, H (2002) Ground state properties of the Nelson Hamiltonian - A Gibbs measure-based approach., Reviews in Mathematical Physics: a journal for survey and expository articles in the field of mathematical physics, 14, pp.173-198, ISSN: 1793-6659. DOI: 10.1142/S0129055X02001119. Lorinczi, J (2002) Gibbs measures on Brownian paths. In Sidoravicius, V (ed) 4th Brazilian School of Probability, IN AND OUT OF EQUILIBRIUM: PROBABILITY WITH A PHYSICS FLAVOR, RIO DE JANEIRO, BRAZIL, pp.349-362, ISBN: 0-8176-4289-7. Lorinczi, J (2002) Gibbs measures on Brownian paths, in In and Out of Equilibrium: Physics with a Probability Flavour, V. Sidoravicius, Ed, Birkhauser. Lorinczi, J, Minlos, RA, Spohn, H (2002) Infrared regular representation of the three dimensional massless Nelson model, Lett Math Phys, 59, pp.189-198, DOI: 10.1023/A:1015528401907. Lorinczi, J, Minlos, RA, Sophn, H (2002) Infrared regular representation of the three dimensionsal massless Nelson model, Lett. Math. Phys, 59, pp.189-198. Lörinczi, J, Minlos, RA, Spohn, H (2002) The infrared behaviour in Nelson's model of a quantum particle coupled to a massless scalar field, Annales Henri Poincare, 3(2), pp.269-295, ISSN: 1424-0637. DOI: 10.1007/s00023-002-8617-6. Lorinczi, J (2002) Towards a theory of renormalization: Renormalization through disagreement percolation, RIMS Kyoto Kokyuroku, 1275, pp.18-30. Lorinczi, J and Minlos, RA (2001) Gibbs measures for Brownian paths under the effect of an external and a small pair potential, J Stat Phys, 105(3), pp.605-648, DOI: 10.1023/A:1012279826414. Lorinczi, J and Minlos, RA (2001) Gibbs measures for Brownian paths under the effect of an external and small pair potential, J. Stat. Phys, 105, pp.605-647. Lorinczi, J (2001) Qualitative properties of the ground state in Nelson's scalar field model - A Gibbs measure-based approach. In eds, AACCEA (ed) Disordered and Complex Systems, London 2000, pp.203-208. Lorinczi, J, Maes, C, Vande Velde, K (1998) Transformations of Gibbs measures, Probab. Theory Rel. Fields, 112, pp.121-147, DOI: 10.1007/s004400050185. Lorinczi, J (1998) Non-Gibbsianness of the reduced SOS-measure, Stoch. Proc. Appl, 74, pp.83-88, DOI: 10.1016/S0304-4149(97)00107-5. Lorinczi, J and Maes, C (1997) Weakly Gibbsian measure for lattice spin systems, J. Stat. Phys, 89, pp.561-579, DOI: 10.1007/BF02765536. van Enter, ACD and Lorinczi, J (1996) Robustness of the non-Gibbsian property: some examples, J. Phys. A: Math. Gen, 29, pp.2465-2473, DOI: 10.1088/03054470/29/10/024. Lorinczi, J (1995) On Limits of the Gibbsian Formalism in Thermodynamics, Groningen, ISBN: 978-90-367-3002-0. Lorinczi, J (1995) Quasilocality of projected Gibbs measures through analyticity techniques, HELVETICA PHYSICA ACTA, 68(7-8), pp.605-626, ISSN: 0018-0238. Lorinczi, J (1995) Quasilocality of projected Gibbs measures through analyticity techniques, Helv. Phys. Acta, 68(7/8), pp.605-626. Lorinczi, J and Vande Velde, K (1994) A note on the projection of Gibbs measures, J. Stat. Phys, 77(3/4), pp.881-887. Lorinczi, J (1994) Some results on the projected two-dimensional Ising model in. In 1993, Leuven, Belgium, Proceedings of the NATO Advanced Workshop 'On Three Levels', tba, pp.373-380. Lorinczi, J and Winnink, M (1993) Some results on almost Gibbs states. In eds, NBEA (ed) Les Houches, 1992, Proceedings of the NATO Advanced Studies Institute Workshop on Cellular Automata and Cooperative Systems, Kluwer, pp.423-432. Lorinczi, J, Harko, T, Todor, E (1988) Kinetical modelling of tumour growth processes. In Proceedings of the 12th Symposium of Computer Sciences, tba, Timisoara.