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 dimensionABSPSPDF

 

Research papers

2018
Time-time covariance for last passage percolation with generic initial profile, with Alessandra Occelli,  arXiv:1807.02982, preprint (2018).ABSPSPDF
2017
Finite GUE distribution with cut-off at a shock, J. Stat. Phys. 172 (2018), 505-521.ABSPSPDF
Limit law of a second class particle in TASEP with non-random initial condition, with Peter Nejjar and Promit Ghosal, arXiv:1710.02323 (2017); to appear in Ann. Inst. H. Poincaré Probab. Statist.ABSPSPDF
Speed and fluctuations for some driven dimer models, with Sunil Chhita and Fabio Toninelli, arXiv:1705.07641, preprint (2017); To appear in Ann. Inst. H. Poincaré D.ABSPSPDF
Universality of the GOE Tracy-Widom distribution for TASEP with arbitrary particle density, with Alessandra Occelli, Electron. J. Probab., 23 (2018), no. 51, 1-24.ABSPSPDF
2016
Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes, with Alexei Borodin and Ivan Corwin, Probab. Theory Relat. Fields172 (2018), 245-321.ABSPSPDF
Limit distributions for KPZ growth models with spatially homogeneous random initial conditions, with Sunil Chhita and Herbert Spohn, Ann. Appl. Probab., 28 (2018), 1573-1603.ABSPSPDF
The hard-edge tacnode process for Brownian motion, with Bálint Vető, Eletron. J. Probab., 22 (2017), no. 79, 1-32.ABSPSPDF
Fluctuations of the competition interface in presence of shocks, with Peter Nejjar, ALEA, Lat. Am. J. Probab. Math. Stat.14 (2017), 299-325.ABSPSPDF
On time correlations for KPZ growth in one dimension, with Herbert Spohn, SIGMA12 (2016), 074.ABSPSPDF
2015

A combinatorial identity for the speed of growth in an anisotropic KPZ model, with Sunil Chhita, Ann. Inst. H. Poincaré D4 (2017), 453-477.

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Random tilings and Markov chains for interlacing particles, with Alexei Borodin, Markov Processes Relat. Fields24 (2018), no. 3.ABSPSPDF
Brownian motions with one-sided collisions: the stationary case, with Herbert Spohn and Thomas Weiss,  Electron. J. Probab.20 (2015), 1-41.ABSPSPDF
2014
Shock fluctuations in flat TASEP under critical scaling, with Peter Nejjar, J. Stat. Phys.60 (2015), 985-1004.ABSPSPDF
Height fluctuations for the stationary KPZ equation, with Alexei Borodin, Ivan Corwin, and Bálint Vető, Math. Phys. Anal. Geom. (2015), 18:20.ABSPSPDF
KPZ universality class and the anchored Toom interface, with Gerard Barkema, Joel Lebowitz and Herbert Spohn, Phys. Rev. E90 (2014), 042116.ABSPSPDF
2013
Tracy-Widom asymptotics for q-TASEP, with Bálint Vető,  Ann. Inst. H. Poincaré Probab. Statist.51 (2015), 1465-1485.ABSPSPDF
Coupled Kardar-Parisi-Zhang equations in one dimension, with Tomohiro Sasamoto and Herbert Spohn, J. Stat. Phys.153 (2013), 377-399.ABSPSPDF
Scaling limit for Brownian motions with one-sided collisions, with Herbert Spohn and Thomas Weiss, Ann. Appl. Probab.25 (2015), 1349-1382.ABSPSPDF
Anomalous shock fluctuations in TASEP and last passage percolation models, with Peter Nejjar, Probab. Theory Relat. Fields61 (2015), 61-109.ABSPSPDF
2012
Perturbed GUE Minor Process and Warren’s Process with Drifts, with René Frings, J. Stat. Phys.154 (2014), 356-377.ABSPSPDF
On the spatial persistence for Airy processes, with René Frings, J. Stat. Mech. (2013), P02001.ABSPSPDF
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.ABSPSPDF
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.ABSPSPDF
2011
Non-colliding Brownian bridges and the asymmetric tacnode process, with Bálint Vető, Electron. J. Probab.17 (2012), no. 44, 1-17.ABSPSPDF
Finite time corrections in KPZ growth models, with René Frings; J. Stat. Phys.144 (2011), 1123-1150.ABSPSPDF
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.ABSPSPDF
On the partial connection between random matrices and interacting particle systems, with René Frings; J. Stat. Phys.141 (2010), 613-637.ABSPSPDF
Limit processes for TASEP with shocks and rarefaction fans, with Ivan Corwin and Sandrine Péché, J. Stat. Phys.140 (2010), 232-267.ABSPSPDF
Universality of slow decorrelation in KPZ growth, with Ivan Corwin and Sandrine Péché, Ann. Inst. H. Poincaré B48 (2012), 134-150.ABSPSPDF
2009
Limit process of stationary TASEP near the characteristic line, with Jinho Baik and Sandrine Péché, Comm. Pure Appl. Math63 (2010), 1017-1070.ABSPSPDF
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.ABSPSPDF
Two speed TASEP, with Alexei Borodin and Tomohiro Sasamoto, J. Stat. Phys.137 (2009), 936-977.ABSPSPDF
2008
Airy processes with wanderers and new universality classes, with Mark Adler and Pierre Van Moerbeke, Ann. Probab.38 (2010), 714-769.ABSPSPDF
Anisotropic growth of random surfaces in 2+1 dimensions: fluctuations and covariance structure, with Alexei Borodin, J. Stat. Mech. (2009), P02009.ABSPSPDF
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.ABSPSPDF
Slow decorrelations in KPZ growth, J. Stat. Mech. (2008), P07022.ABSPSPDF
Anisotropic growth of random surfaces in 2+1 dimensions, with Alexei Borodin, Comm. Math. Phys.325 (2014), 603-684.ABSPSPDF
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.ABSPSPDF
Large time asymptotics of growth models on space-like paths I: PushASEP, with Alexei Borodin, Electron. J. Probab.13 (2008), 1380-1418.ABSPSPDF
Transition between Airy1 and Airy2 processes and TASEP fluctuations, with Alexei Borodin and Tomohiro Sasamoto, Comm. Pure Appl. Math.61 (2008), 1603-1629.ABSPSPDF
2006
Fluctuations in the discrete TASEP with periodic initial configurations and the Airy1 process, with Alexei Borodin and Michael Prähofer, Int. Math. Res. Papers2007, rpm002 (2007).ABSPSPDF
Fluctuation properties of the TASEP with periodic initial configuration, with Alexei Borodin, Michael Prähofer and Tomohiro Sasamoto, J. Stat. Phys.129 (2007), 1055-1080.ABSPSPDF
Domino tilings and the six-vertex model at its free fermion point, with Herbert Spohn, J. Phys. A: Math. Gen.39 (2006), 10297-10306.ABSPSPDF
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.ABSPSPDF
A determinantal formula for the GOE Tracy-Widom distribution, with Herbert Spohn, J. Phys. A, Math. Gen.38 (2005), L557-L561.ABSPSPDF
2004
Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues, Comm. Math. Phys.252 (2004), 77-109.ABSPSPDF
2003
Constrained Brownian motion: fluctuations away from circular and parabolic barriers, with Herbert Spohn, Ann. Probab.33 (2005), 1302-1325.ABSPSPDF
Fluctuations of an Atomic Ledge Bordering a Crystalline Facet, with Michael Prähofer and Herbert Spohn, Phys. Rev. E, Rapid Communications 69 (2004), 035102(R).ABSPSPDF
2002
Step fluctuations for a faceted crystal, with Herbert Spohn, J. Stat. Phys.113 (2003), 1-46.ABSPSPDF
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].ABSPSPDF
Last Branching in Directed Last Passage Percolation, with Herbert Spohn, Markov Process and Related Fields 9 (2003), 323-339.ABSPSPDF

 

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.ABSPSPDF
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.ABSPSPDF

 

Reviews

From interacting particle systems to random matrices, Contribution to StatPhys24 special issue, J. Stat. Mech. (2010), P10016.ABSPSPDF
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.ABSPSPDF
One-dimensional stochastic growth and Gaussian ensembles of random matrices, with Michael Prähofer; In proceedings of ''Inhomogeneous Random Systems 2005'', Markov Processes Relat. Fields http://math-mprf.org/journal/articles/id1077/12 (2006), 203-234.ABSPSPDF

 

Short reviews and proceedings

Limit distributions for KPZ growth models with spatially homogeneous random initial conditions, in Oberwolfach Report13 (2016), 3031–3086.PSPDF
Height fluctuations for the stationary KPZ equation, in Oberwolfach Report11 (2014), 1560-1563.PSPDF

Anomalous shock fluctuations in TASEP, in Oberwolfach Report 10 (2013), 3059-3062.PSPDF
Interacting particle systems and random matrices, in Oberwolfach Report7 (2010), 2915–2918.PSPDF
Around the universality of the Airy1 process, in Oberwolfach Report4 (2007), 2484-2486.PSPDF
The Airy1 and Airy2 processes in the TASEP, in Oberwolfach Report3 (2006), 2473-2476.PSPDF
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.ABSPSPDF

 

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, Durham University, UK
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.ABSPSPDF
Dall'informatica alla geometria ortogonale passando per l'algebra universale, con R. Moresi, Note di Matematica e Fisica, CERFIM 11 (2000), 115-140.PSPDF
Contact Matrices for Random Walks,diploma thesis supervised by Joel L. Lebowitz.PSPDF
Notes basées sur le cours du Prof. Amrein's (Unige): Théorie des groupes pour la physique.PSPDF
Project d'ingénieur: a computer program for the computation of lattices.PSPDF
Project STS sur les nombres complexes.PSPDF