Probability and Stochastic Analysis - University of Bonn
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
Aztec Diamond
The Aztec Diamond

PhD thesis

Shape fluctuation of crystal facets and surface growth in one dimension ABS PS PDF

Research papers

2017
Limit law of a second class particle in TASEP with non-random initial condition, with Peter Nejjar and Promit Ghosal, arXiv:1710.02323, preprint (2017)ABS PS PDF
Speed and fluctuations for some driven dimer models, with Sunil Chhita and Fabio Toninelli, arXiv:1705.07641, preprint (2017)ABS PS PDF
Universality of the GOE Tracy-Widom distribution for TASEP with arbitrary particle density, with Alessandra Occelli, arXiv:1704.01291, preprint (2017)ABS PS PDF
2016
Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes, with Alexei Borodin and Ivan Corwin, Probab. Theory Relat. Fields (2017), online first.ABS PS PDF
Limit distributions for KPZ growth models with spatially homogeneous random initial conditions, with Sunil Chhita and Herbert Spohn, arXiv:1611.06690, preprint (2016); to appear in Ann. Appl. Probab.ABS PS PDF
The hard-edge tacnode process for Brownian motion, with Bálint Vető, Eletron. J. Probab., 22 (2017), no. 79, 1-32ABS PS PDF
Fluctuations of the competition interface in presence of shocks, with Peter Nejjar, ALEA, Lat. Am. J. Probab. Math. Stat. 14 (2017), 299-325ABS PS PDF
On time correlations for KPZ growth in one dimension, with Herbert Spohn, SIGMA 12 (2016), 074 ABS PS PDF
2015
A combinatorial identity for the speed of growth in an anisotropic KPZ model, with Sunil Chhita, arXiv:1508.01665, preprint (2015); to appear in in Ann. Inst. H. Poincaré D ABS PS PDF
Random tilings and Markov chains for interlacing particles, with Alexei Borodin, arXiv:1506.03910, preprint (2015) ABS PS PDF
Brownian motions with one-sided collisions: the stationary case, with Herbert Spohn and Thomas Weiss,  Electron. J. Probab. 20 (2015), 1-41 ABS PS PDF
2014
Shock fluctuations in flat TASEP under critical scaling, with Peter Nejjar, J. Stat. Phys. 60 (2015), 985-1004 ABS PS PDF
Height fluctuations for the stationary KPZ equation, with Alexei Borodin, Ivan Corwin, and Bálint Vető, Math. Phys. Anal. Geom. (2015), 18:20 ABS PS PDF
KPZ universality class and the anchored Toom interface, with Gerard Barkema, Joel Lebowitz and Herbert Spohn, Phys. Rev. E 90 (2014), 042116 ABS PS PDF
2013
Tracy-Widom asymptotics for q-TASEP, with Bálint Vető,  Ann. Inst. H. Poincaré Probab. Statist. 51 (2015), 1465-1485 ABS PS PDF
Coupled Kardar-Parisi-Zhang equations in one dimension, with Tomohiro Sasamoto and Herbert Spohn, J. Stat. Phys. 153 (2013), 377-399 ABS PS PDF
Scaling limit for Brownian motions with one-sided collisions, with Herbert Spohn and Thomas Weiss, Ann. Appl. Probab. 25 (2015), 1349-1382 ABS PS PDF
Anomalous shock fluctuations in TASEP and last passage percolation models, with Peter Nejjar, Probab. Theory Relat. Fields 61 (2015), 61-109 ABS PS PDF
2012
Perturbed GUE Minor Process and Warren’s Process with Drifts, with René Frings, J. Stat. Phys. 154 (2014), 356-377 ABS PS PDF
On the spatial persistence for Airy processes, with René Frings, J. Stat. Mech. (2013), P02001 ABS PS PDF
Convergence of the two-point function of the stationary TASEP, with Jinho Baik and Sandrine Péché, In Singular Phenomena and Scaling in Mathematical Models (2014), 91-110 ABS PS PDF
Free energy fluctuations for directed polymers in random media in 1+1 dimension, with Alexei Borodin and Ivan Corwin, Comm. Pure Appl. Math. 67 (2014), 1129–1214 ABS PS PDF
2011
Non-colliding Brownian bridges and the asymmetric tacnode process, with Bálint Vető, Electron. J. Probab. 17 (2012), no. 44, 1-17 ABS PS PDF
Finite time corrections in KPZ growth models, with René Frings; J. Stat. Phys. 144 (2011), 1123-1150 ABS PS PDF
2010
Non-intersecting random walks in the neighborhood of a symmetric tacnode, with Mark Adler and Pierre Van Moerbeke, Ann. Probab. 41 (2013), 2599–2647 ABS PS PDF
On the partial connection between random matrices and interacting particle systems, with René Frings; J. Stat. Phys. 141 (2010), 613-637 ABS PS PDF
Limit processes for TASEP with shocks and rarefaction fans, with Ivan Corwin and Sandrine Péché, J. Stat. Phys. 140 (2010), 232-267 ABS PS PDF
Universality of slow decorrelation in KPZ growth, with Ivan Corwin and Sandrine Péché, Ann. Inst. H. Poincaré B 48 (2012), 134-150 ABS PS PDF
2009
Limit process of stationary TASEP near the characteristic line, with Jinho Baik and Sandrine Péché, Comm. Pure Appl. Math 63 (2010), 1017-1070 ABS PS PDF
Maximum of Dyson Brownian motion and non-colliding systems with a boundary, with Alexei Borodin, Michael Prähofer, Tomohiro Sasamoto and Jon Warren, Electron. Comm. Probab. 14 (2009), 486-494 ABS PS PDF
Two speed TASEP, with Alexei Borodin and Tomohiro Sasamoto, J. Stat. Phys. 137 (2009), 936-977 ABS PS PDF
2008
Airy processes with wanderers and new universality classes, with Mark Adler and Pierre Van Moerbeke, Ann. Probab. 38 (2010), 714-769 ABS PS PDF
Anisotropic growth of random surfaces in 2+1 dimensions: fluctuations and covariance structure, with Alexei Borodin, J. Stat. Mech. (2009), P02009 ABS PS PDF
The Airy1 process is not the limit of the largest eigenvalue in GOE matrix diffusion, with Folkmar Bornemann and Michael Prähofer, J. Stat. Phys. 133 (2008), 405-415 ABS PS PDF
Slow decorrelations in KPZ growth, J. Stat. Mech. (2008), P07022 ABS PS PDF
Anisotropic growth of random surfaces in 2+1 dimensions, with Alexei Borodin, Comm. Math. Phys. 325 (2014), 603-684 ABS PS PDF
2007
Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP, with Alexei Borodin and Tomohiro Sasamoto, Comm. Math. Phys. 283 (2008), 417-449 ABS PS PDF
Large time asymptotics of growth models on space-like paths I: PushASEP, with Alexei Borodin, Electron. J. Probab. 13 (2008), 1380-1418 ABS PS PDF
Transition between Airy1 and Airy2 processes and TASEP fluctuations, with Alexei Borodin and Tomohiro Sasamoto, Comm. Pure Appl. Math. 61 (2008), 1603-1629 ABS PS PDF
2006
Fluctuations in the discrete TASEP with periodic initial configurations and the Airy1 process, with Alexei Borodin and Michael Prähofer, Int. Math. Res. Papers 2007, rpm002 (2007) ABS PS PDF
Fluctuation properties of the TASEP with periodic initial configuration, with Alexei Borodin, Michael Prähofer and Tomohiro Sasamoto, J. Stat. Phys. 129 (2007), 1055-1080 ABS PS PDF
Domino tilings and the six-vertex model at its free fermion point, with Herbert Spohn, J. Phys. A: Math. Gen. 39 (2006), 10297-10306 ABS PS PDF
2005
Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process, with Herbert Spohn, Comm. Math. Phys. 265 (2006), 1-44 ABS PS PDF
A determinantal formula for the GOE Tracy-Widom distribution, with Herbert Spohn, J. Phys. A, Math. Gen. 38 (2005), L557-L561 ABS PS PDF
2004
Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues, Comm. Math. Phys. 252 (2004), 77-109 ABS PS PDF
2003
Constrained Brownian motion: fluctuations away from circular and parabolic barriers, with Herbert Spohn, Ann. Probab. 33 (2005), 1302-1325 ABS PS PDF
Fluctuations of an Atomic Ledge Bordering a Crystalline Facet, with Michael Prähofer and Herbert Spohn, Phys. Rev. E, Rapid Communications 69 (2004), 035102(R) ABS PS PDF
2002
Step fluctuations for a faceted crystal, with Herbert Spohn, J. Stat. Phys. 113 (2003), 1-46 ABS PS PDF
Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices, with Joel L. Lebowitz, J. Phys. A: Math. Gen. 36 (2003), 5719-5730; Appendix with the complete mathematical proof of Proposition 4.2 [ps] ABS PS PDF
Last Branching in Directed Last Passage Percolation, with Herbert Spohn, Markov Process and Related Fields 9 (2003), 323-339 ABS PS PDF

Books & co.

Reflected Brownian motions in the KPZ universality class, Springer Brief, with Herbert Spohn and Thomas Weiss available here   
Random Growth Models, with Herbert Spohn arXiv:1003.0881 (2010). One chapter of the The Oxford Handbook of Random Matrix Theory ABS PS PDF
Dimers and orthogonal polynomials: connections with random matrices, Extended lecture notes of the minicourse at IHP (5-7 Oct. 2009), arXiv:1004.3212 (2010).  Published as part of Dimer Models and Random Tilings, Panoramas et synthèses 45 (2015), B. de Tilière, P. Ferrari, edited by C. Boutillier, N. Enriquez. ABS PS PDF

Reviews

From interacting particle systems to random matrices, Contribution to StatPhys24 special issue, J. Stat. Mech. (2010), P10016 ABS PS PDF
The universal Airy1 and Airy2 processes in the Totally Asymmetric Simple Exclusion Process, In Proceeding ''Integrable Systems and Random Matrices: In Honor of Percy Deift'', Contemporary Mathematics 458 (2008), 321-332 ABS PS PDF
One-dimensional stochastic growth and Gaussian ensembles of random matrices, with Michael Prähofer; In proceedings of ''Inhomogeneous Random Systems 2005'', Markov Processes Relat. Fields 12 (2006), 203-234 ABS PS PDF

Short reviews and proceedings

Limit distributions for KPZ growth models with spatially homogeneous random initial conditions, in Oberwolfach Report ?? (2016), ??-?? PS PDF
Height fluctuations for the stationary KPZ equation, in Oberwolfach Report 11 (2014), 1560-1563 PS PDF

Anomalous shock fluctuations in TASEP, in Oberwolfach Report 10 (2013), 3059-3062 PS PDF
Interacting particle systems and random matrices, in Oberwolfach Report 7 (2010), 2915–2918 PS PDF
Around the universality of the Airy1 process, in Oberwolfach Report 4 (2007), 2484-2486 PS PDF
The Airy1 and Airy2 processes in the TASEP, in Oberwolfach Report 3 (2006), 2473-2476 PS PDF
Stochastic growth in one dimension and Gaussian multi-matrix models, with Michael Prähofer and Herbert Spohn; In proceedings of the ''14th International Congress on Mathematical Physics'' (ICMP 2003), World Scientific (J.-C. Zambrini ed.) (2006), 404-411 ABS PS PDF

Mark Adler, Brandeis University, USA
Jinho Baik, University of Michigan, USA
Gerard Barkema, Universiteit Utrecht, The Netherlands
Alexei Borodin, MIT, USA
Folkmar Bornemann, TU-Munich, Germany
Sunil Chhita, Bonn University, Germany
Ivan Corwin, Columbia University,USA
René Frings, Bonn University, Germany
Joel L. Lebowitz, Rutgers University, USA
Peter Nejjar, ENS Paris, France
Sandrine Péché, Université Paris Diderot, France
Michael Prähofer, TU-Munich, Germany
Tomohiro Sasamoto, Tokyo Institute of Technology, Japan
Herbert Spohn, TU-Munich, Germany
Pierre Van Moerbeke, Université Catholique de Louvain, Belgium
Bálint Vető, Hungarian Academy of Sciences, Hungary
Jon Warren, Warwick University, England
Thomas Weiss, TU-Munich, Germany

Other works

Random matrices and determinantal processes, contributo del ''Colloquio di matematica'', Note di Matematica e Fisica, CERFIM 12 (2003), 67-83 ABS PS PDF
Dall'informatica alla geometria ortogonale passando per l'algebra universale, con R. Moresi, Note di Matematica e Fisica, CERFIM 11 (2000), 115-140 PS PDF
Contact Matrices for Random Walks, diploma thesis supervised by Joel L. Lebowitz PS PDF
Notes basées sur le cours du Prof. Amrein's (Unige): Théorie des groupes pour la physique PS PDF
Project d'ingénieur: a computer program for the computation of lattices PS PDF
Project STS sur les nombres complexes PS PDF