

2001  Diploma in Physics, EPF Lausanne, Switzerland  2004  Dr. rer. nat., TU Munich  2004  2006  Postdoc, TU Munich  2006  2008  Research Position, Weierstrass Institute for Applied Analysis and Stochastics, Berlin  2008  2009  Akademischer Oberrat, University of Bonn  Since 2009  Professor (W2), University of Bonn 


The KPZ universality class of stochastic growth models in 1+1 dimensions consists in models with the same physical properties of the KPZ equation. Through the FeynmanKac representation one sees that the KPZ class includes equilibrium models as directed random polymers as well. The study of special models with a determinantal structure allowed to determine the (conjectural universal) limit processes that describes the fluctuations of interfaces for KPZ models (see e.g. [3,2,1,4]). Along special spacetime lines, correlations decay much more slowly than along spatial directions [12]. This property can be used to study decoupling around shocks [13]. In the last few years the number of solvable models has been extended beyond the class with determinantal correlations, leading to a number of results in agreement with the universality conjecture. For these new models, results are sofar available for onepoint distributions. This is the case for the semidiscrete directed polymer [5], from which results on the distribution function of the solution of the KPZ equations are obtained [6,5].
Nevertheless, showing universality beyond integrability is still a big challenge and results are not as strong as in random matrix theory. The integrable models are an important starting point, as they could be used for perturbation theory, involving renormalization techniques. Further, if one proves universality using probabilistic argument also for nonintegrable models, the identification of the limit processes goes through the solution of the integrable models. One of the major open question (regardless of the model under consideration, i.e., even for models with determinantal structure at fixed time), is the precise description of the limiting process for the timetime correlations.


DFG Collaborative Research Center SFB 611 “Singular Phenomena and Scaling in Mathematical Models”
Principal Investigator of Project A12 “Universality of fluctuations in mathematical models of physics”
DFG Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”
Principal Investigator of Project B04 “Random matrices and random surfaces”


Research Area G My research deals with stochastic models of interacting particle systems and study random variables like the integrated current, which can be seen as height functions of a growing interface with stochastic dynamics. We determined the large time limit processes in the context of the exclusion process [1,2,3] and the spacetime covariance [4]. For models like directed polymers at positive temperature, the random variable to be studied is the free energy [5]. The system under consideration are often discrete, but in the large time limit the fluctuation laws becomes universal. The same laws arise in the KPZ equation, which is a singular equation. Some of the models with a tunable parameter governing the asymmetry of the dynamics, can even be scaled directly to converge to the KPZ equation [6]. Recently we studied also timetime correlations [7], random but not stationary initial conditions [8], the spacetime covariance structure [9] of a 2+1 dimensional model in the anisotropic KPZ class [10], and finally showed universality for flat initial conditions [11]. 


[ 1] Alexei Borodin, Patrik L. Ferrari, Michael Prähofer, Tomohiro Sasamoto
Fluctuation properties of the TASEP with periodic initial configuration J. Stat. Phys. , 129: (56): 10551080 2007[ 2] Alexei Borodin, Patrik L. Ferrari, Tomohiro Sasamoto
Transition between {Airy_1} and {Airy_2} processes and TASEP fluctuations Comm. Pure Appl. Math. , 61: (11): 16031629 2008[ 3] Jinho Baik, Patrik L. Ferrari, Sandrine Péché
Limit process of stationary TASEP near the characteristic line Comm. Pure Appl. Math. , 63: (8): 10171070 2010[ 4] Patrik L. Ferrari, Herbert Spohn
Scaling limit for the spacetime covariance of the stationary totally asymmetric simple exclusion process Comm. Math. Phys. , 265: (1): 144 2006[ 5] Alexei Borodin, Ivan Corwin, Patrik Ferrari
Free energy fluctuations for directed polymers in random media in 1+1 dimension Comm. Pure Appl. Math. , 67: (7): 11291214 2014[ 6] Alexei Borodin, Ivan Corwin, Patrik Ferrari, Bálint Vetö
Height fluctuations for the stationary KPZ equation Math. Phys. Anal. Geom. , 18: (1): Art. 20, 95 2015[ 7] Patrik L. Ferrari, Herbert Spohn
On time correlations for KPZ growth in one dimension SIGMA Symmetry Integrability Geom. Methods Appl. , 12: : Paper No. 074, 23 2016[ 8] S. Chhita, P.L. Ferrari, H. Spohn
Limit distributions for KPZ growth models with spatially homogeneous random initial conditions preprint: arXiv:1611.06690; To appear in Ann. Appl. Probab. 0[9] A. Borodin, I. Corwin, P.L. Ferrari
Anisotropic (2+1)d growth and Gaussian limits of qWhittaker processes preprint, arXiv:1612.00321; To appear in Probab. Theory Relat. Fields 0 [10] Alexei Borodin, Patrik L. Ferrari
Anisotropic growth of random surfaces in 2+1 dimensions Comm. Math. Phys. , 325: (2): 603684 2014 [ 11] P.L. Ferrari, A. Occelli
Universality of the GOE TracyWidom distribution for TASEP with arbitrary particle density preprint, arXiv:1704.01291 0[12] Ivan Corwin, Patrik L. Ferrari, Sandrine Péché
Universality of slow decorrelation in KPZ growth Ann. Inst. Henri Poincaré Probab. Stat. , 48: (1): 134150 2012 [ 13] Patrik L. Ferrari, Peter Nejjar
Anomalous shock fluctuations in TASEP and last passage percolation models Probab. Theory Related Fields , 161: (12): 61109 2015[ 14] Patrik L. Ferrari, Herbert Spohn
Step fluctuations for a faceted crystal J. Statist. Phys. , 113: (12): 146 2003




• Annals of Applied Probability (since 2013)
• Mathematical Physics, Analysis and Geometry (since 2013)


2001  Award for the second best general exams average of the complete academic program at EPFL (over all departments)  2004  Distinction “Summa Cum Laude” for the PhD thesis  2009  Heinz MaierLeibnitz Prize 2009 of the German Research Foundation (DFG) 


2008  Lecture of 11.5h on Random Matrices and Related Problems at the Beg Rohu Summer School in Bretagne, France  2009  Minicourse of 4h on Dimers and orthogonal polynomials: connections with random matrices at the Workshop Dimer models and random tilings, Institut Henri Poincaré, Paris, France  2011  Short lecture of 6h on Random Matrices and Interacting Particle Systems at the Finnish Center of Excellence in Analysis and Dynamics Research, Helsinki, Finland  2013  Minicourse at the School/Workshop “Random Matrices and Growth Models”, ICTP, Trieste, Italy  2013  Advanced course at the Alea in Europe School, Marseille, France 


2008  Professor (W2), University of Bochum  2008  Professor (W2), University of Bonn  2011  Professor (W3), University of Leipzig 


René Frings (2014): “Interlacing Patterns in Exclusion Processes and Random Matrices”
Peter Nejjar (2015): “Shock Fluctuations in KPZ Growth Models”,
now Postdoc, Institute of Science and Technology, Austria


 Master theses: 15, currently 1
 Diplom theses: 8
 PhD theses: 2, currently 1


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