Books :

T. Komorowski, C. Landim, S. Olla : Fluctuations in Markov Processes, martingale approximation and time symmetry . Grundlehren der Mathematischen Wissenschaften 345, Springer, August 31, 2012.

Some Publications

·       Non-equilibrium isothermal transformations in a temperature gradient from a microscopic dynamics, (2015), Stefano OllaViviana Letizia, arXiv:1505.05002 [pdfpsother]


·       Superdiffusion of energy in a chain of harmonic oscillators with noise, Milton JaraTomasz KomorowskiStefano Olla, to appear in Comm.Math.Phys. (2015), arXiv:1402.2988 [pdfps]


·       Microscopic derivation of an adiabatic thermodynamic transformation, Stefano OllaMarielle Simon, Braz. J. Probab. Stat. 29 (2015), no. 2, 540-564. doi: 10.1214/14-BJPS275.


·       Green-Kubo formula for weakly coupled system with dynamical noise, Cedric BernardinFrancois HuveneersJoel L. LebowitzCarlangelo LiveraniStefano Olla, Comm.Math.Phys., 334, n.3, 1377-1412, March 2015. DOI 10.1007/s00220-014-2206-7. arXiv:1311.7384 [pdfpsother]


·       Microscopic Derivation of an Isothermal Thermodynamic Transformation, in From Particle Systems to Partial Differential Equations, C. Bernardin and  P. Goncalvez, Springer Proceedings in Mathematics and Statistics 75, Springer-Verlag Berlin Heidelberg, 2014. DOI 10.1007/978-3-642-54271-8,,


·       Energy Diffusion in Harmonic System with Conservative Noise, Giada Basile, Stefano Olla, J.Stat.Phys, 155, 6, 1126-1142, 2014. DOI 10.1007/s10955-013-0908-4


·       Asymptotics of the solutions of the stochastic lattice wave equation, Tomasz Komorowski, Stefano Olla, Lenya Ryznik, Arch.Rat.Mech.Appl., 209, 455-494, 2013. 


·       Energy Diffusion in anharmonic chain with conservative noise, Stefano Olla, Makiko Sasada, Prob.Th.Rel.Fields, 157, 721—775, (2013), DOI 10.1007/s00440-012-0469-5,,


·       Effective velocity and Einstein relation for a random walk in a Galton-Watson random tree, G. Benarous, Y. Hu, S. Olla, O. Zeitouni, Ann. Inst. H. Poincaré, Prob. Stat., 49, N. 3, 698-721, 2013.


·       Toward the Fourier law for a weakly interacting anharmonic crystal, Carlangelo Liverani, Stefano Olla, J.Am.Math.Soc. 25, N.2, 555-583, 2012. arXiv:1006.2900 [pdf].


·       Transport Properties of a Chain of Anharmonic Oscillators with random flip of velocities, C. Bernardin, Stefano Olla, J.Stat.Phys. 145, 1224-1255, 2011. arXiv:1105.0493 [pdfpsother]


·       Negative Thermal Conductivity in Rotor model, A. Iacobucci, F. Legoll, S Olla, G. Stoltz, Phys.Rev.E 84, 061108, 2011. arXiv:1107.1766 [pdfpsother]



·       Thermal Conductivity of the Toda Lattice with Conservative Noise, A. Iacobucci, F. Legoll, Stefano Olla, Gabriel Stolz, J. Stat. Phys. 140, 2, 2010, 336--348,

·       A limit theorem for an additive functionals of Markov Chains, Milton Jara, Tomasz Komorowski, Stefano Olla, Gabriel Stolz, Annals of Applied Probability 19, No 6,  2270-2300, 2009, DOI: 10.1214/09-AAP610. arXiv:0809.0177 [pdf]


·       Energy diffusion and superdiffusion in oscillators lattice networks, Stefano Olla, proceedings of ICMP RIO 06,


·       Heat Conduction and Entropy Production in Anharmonic Crystals with Self-Consistent Stochastic Reservoirs, Federico Bonetto, Joel L. Lebowitz, Jani Lukkarinen, Stefano Olla, J. Stat. Phys. 134, 5, 2009, 1097--1119,

Energy transport in stochastically perturbed lattice dynamics Giada Basile, Stefano Olla, Herbert Spohn, Arch.Rat.Mech., Vol. 195, no. 1, 171-203, 2009.

·       Stationary and non-equilibrium fluctuations in boundary driven exclusion processes, Claudio Landim, Aniura Milanés, Stefano Olla, Markov Proc. Rel Fields, vol. 14, 165-184, 2008

Anomalous transport and relaxation in classical one-dimensional models, G. Basile, L. Delfini, S. Lepri, R. Livi, S. Olla, A. Politi, European Journal of Physics Special Topics,  vol.151, 85–93, 2007.

·       Thermal conductivity for a momentum conserving model, G. Basile, C. Bernardin, S. Olla, Comm. in Mathematical Physics, 287, 1, 67-98, 2009.

Momentum conserving model with anomalous thermal conductivity in low dimensional systems, G. Basile, C. Bernardin, S. Olla, Phys.Rev.Lett. 96, 204303 (2006),

·       Fourier's law for a microscopic model of heat conduction, C.Bernardin, S. Olla, Journal of Statistical Physics, vol.118, nos.3/4, 271-289, (2005), pdf.

Equilibrium Fluctuations for a system of harmonic oscillators with conservative noise, J. Fritz, K. Nagy, S.Olla, Journal of Statistical Physics, vol. 122, no.3, 399-415, 2006. pdf.

·       Fluctuations in the weakly asymmetric exclusion process with open boundary conditions, B. Derrida, C. Enaud, C. Landim, S.Olla, Journal of Statistical Physics. Vol. 118, Nos. 5/6, March 2005, 795 - 811. pdf.

On mobility and Einstein relation for tracer particles in time mixing random environments, T. Komorowski, S. Olla, Journal of Statistical Physics,  Vol. 118, Nos. 3/4, February 2005.  pdf

·       Einstein relation for random walk on random environment, T. Komorowski, S. Olla, Stochastic Processes and Applications. vol. 115, 1279-1301, 2005. pdf.

 On the viscosity and  fluctuation-dissipation in exclusion processes.  C.Landim, S. Olla, S.R.S.Varadhan, Journal of Statistical Physics, vol.115, N.1/2, 323-363 (Avril 2004). pdf

·       Homogenization of a bond diffusion in a locally ergodic random environment, S. Olla, P. Siri, Stochastic Processus and Application, vol.109, 317-326, 2004. pdf

Diffusive behaviour of the equilibrium  fluctuations in the asymmetric exclusion processes, C.Landim, S. Olla, S.R.S.Varadhan, in Stochastic Analysis on Large Interacting Systems, Advanced Studies in Pure Mathematics vol. 39 (T. Funaki, H. Osada editors), March 2004, Mathematical Society of Japan. pdf

·       Equilibrium Fluctuations for Interacting Ornstein-Uhlenbeck particles, S. Olla, C. Tremoulet, Commun.Math.Phys, vol. 233, 463-491, 2003. pdf

A note on the central limit theorem for two-fold stochastic random walks in a random environment, T. Komorowski, S. Olla, Bull. Pol. Acad. Sci., vol 51 (2), 2003. pdf

·       On the Sector Condition and Homogenization of Diffusions with a Gaussian Drift, T. Komorowski, S. Olla, J. Funct. Anal., vol. 197, no.1, 179-211, 2003. pdf

Invariant measure for Passive Tracer in Ornstein-Uhlenbeck flows, T. Komorowski, S. Olla, Stochastic Processes and Applications, vol. 105, n.1, 139-173, 2003.  pdf

·       On the Superdiffusive Behavior of Passive Tracer  with a Gaussian Drift,  T. Komorowski, S. Olla, december 2001,  J.Stat.Phys., vol. 108, Nos. 3/4, 647-668, 2002. pdf

Asymptotic Behaviour of a Tagged Particle in Simple Exclusion Processes. C.Landim, S. Olla, S.R.S.Varadhan. Bol. Soc. Bras. Mat., vol 31, No.3, 241-275, 2000. pdf

·       Notes on the Central Limit Theorems for Tagged Particles and Diffusions in Random Fields. Notes of the course given at Etàts de la recherche: Milieux Alèatoires , CIRM 23-25 November 2000. Milieux Alèatoires (F. Comtes, E. Pardoux editors)Panorama et Synthèses 12, 75-100, 2001.  pdf 

Symmetric Simple Exclusion: Regularity of the Self-Diffusion coefficient. C.Landim, S. Olla, S.R.S.Varadhan. Comm.Math.Phys. (2001), vol. 224, 302-321 (2001).  pdf

·       Finite-Dimensional Approximation of the Self-Diffusion coefficient for the Exclusion Process. C.Landim, S. Olla, S.R.S.Varadhan. Annals of Probability. vol. 30, No. 2, 1-26, (2002), pdf.

Diffusive behaviour of interacting particles systems, Monte Carlo Methods and Applications, Vol. 7, No. 3-4, pp. 329-338, (2001). dvi , ps .

·       Fluctuation for Weakly Massive Interface Model and Applications to the Interface on a Wall. T.Funaki, S. Olla, Stochastic Processes and Appl., Vol. 94, 1-27, (2001) pdf.

On Homogenization of Time Dependent Random Flows. T. Komorowski, S. Olla, Probability Theory and Related Fields. vol. 121, 98-116, (2001). pdf.

·       Equilibrium Fluctuation of Asymmetric Simple Exclusion processes in Dimension, C.C. Chang, C. Landim, S. Olla, Probability Theory and Related Fields, Vol. 119, 381-409, (2001).  pdf.

Equilibrium Fluctuation for a Ginzburg-Landau Interface Model, G.B. Giacomin, S. Olla, H. Spohn, Annals of Probability. Vol. 29, No. 3, 1138-1172, (2001). pdf.

·       Driven Tracer Particle in One-Dimensional Symmetric Simple Exclusion, C. Landim, S. Olla, S.B. Volchan, Comm.Math.Phys., vol.192, 287-307 (1998). pdf.

Homogenization of Convection-Diffusion Equation with Space-Time Ergodic Random Flow., C. Landim, S. Olla H.T. Yau, Probability Theory and Related Fields, vol.112, 203-220 (1998). pdf .

·       Driven Tracer and Einstein Relation in One-Dimensional Symmetric Simple Exclusion, C. Landim, S. Olla S.B. Volchan, Resenhas do Instituto de Matematica e Estatistica da Universidade de Sao Paulo, vol.3, N.2, 173-209, (1997). dvi , ps

Microscopic derivation of the Cahn-Hilliard equations, L.Bertini, C. Landim, S.Olla, J.Stat.Physics, vol.88, Nos.1/2, 365-381, (1997). ps .

·       Reversibility in Infinite Hamiltonian Systems with Conservative Noise, J. Fritz, C. Liverani, S. Olla, Comm. Math. Phys. vol.189, 481-496, (1997) pdf .

Properties of the diffusion coefficients for the Asymmetric Simple Exclusion Processes. C. Landim, S. Olla, H.T. Yau, Annals of Probability, vol.24, n.4, 1779-1808 (1997). ps.

·       First Order Correction for the Hydrodynamic Limit of Asymmetric Simple Exclusion Processes in dimension d > 2 C. Landim, S. Olla, H.T. Yau, Comm. Pure and Applied Math. vol.50, n.2, 149-203 (1997) ps.

Ergodicity of Infinite Hamiltonian Systems with Conservative Noise, C. Liverani, S. Olla, Probability Theory and Related Fields, n.106, 401-445 (1996). pdf.

·       Lectures on Homogenization of Diffusion Processes in Random Fields, S. Olla, publications de l'Ecole Doctorale de l'Ecole Polytechnique, (1994).  ps,  dvi.

Macroscopic Properties of a Stationary Non-Equilibrium Distribution for a Non-Gradient Interacting Particles System, C. Kipnis, C. Landim, S. Olla, Ann. Inst. H. Poincare, probabilites et statistiques 31, n.1, (1995). ps.

·       Hydrodynamic Limits and Ergodicity for Hamiltonian Systems with small noise, S. Olla, in "Cellular Automata and Cooperative Systems", Boccara et al. editors, Nato Asi series, Kluwer Academic Pub. (1993).

Hydrodynamic Limit for a Non-Gradient System: the Generalised Symmetric Exclusion Process, C. Kipnis, C. Landim, S. Olla, Comm. Pure Appl. Math. 47 n.11, 1475-1545 (1994). ps.

·       Hydrodynamic Limit for a Hamiltonian System with Weak Noise, S. Olla, H.T. Yau, S.R.S. Varadhan, Comm. Math. Phys. 155, 523-560 (1993).pdf , dvi

Scaling Limit for Interacting Ornstein-Uhlenbeck Processes, S. Olla, S.R.S. Varadhan, Comm.Math.Phys. 135, 335-378 (1991). pdf

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