PhD thesis

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Shape fluctuation of crystal facets and surface growth in one dimension

Research papers

2017
•	Speed and fluctuations for some driven dimer models, with Sunil Chhita and Fabio Toninelli, arXiv:1705.07641, preprint (2017)
•	Universality of the GOE Tracy-Widom distribution for TASEP with arbitrary particle density, with Alessandra Occelli, arXiv:1704.01291, preprint (2017)
2016
•	Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes, with Alexei Borodin and Ivan Corwin, arXiv:1612.00321, preprint (2016)
•	Limit distributions for KPZ growth models with spatially homogeneous random initial conditions, with Sunil Chhita and Herbert Spohn, arXiv:1611.06690, preprint (2016)
•	The hard-edge tacnode process for Brownian motion, with Bálint Vető, arXiv:1608.00394, preprint (2016)
•	Fluctuations of the competition interface in presence of shocks, with Peter Nejjar, arXiv:1603.07498, preprint (2016)
•	On time correlations for KPZ growth in one dimension, with Herbert Spohn, SIGMA 12 (2016), 074
2015
•	A combinatorial identity for the speed of growth in an anisotropic KPZ model, with Sunil Chhita, arXiv:1508.01665, preprint (2015)
•	Random tilings and Markov chains for interlacing particles, with Alexei Borodin, arXiv:1506.03910, preprint (2015)
•	Brownian motions with one-sided collisions: the stationary case, with Herbert Spohn and Thomas Weiss,  Electron. J. Probab. 20 (2015), 1-41
2014
•	Shock fluctuations in flat TASEP under critical scaling, with Peter Nejjar, J. Stat. Phys. 60 (2015), 985-1004
•	Height fluctuations for the stationary KPZ equation, with Alexei Borodin, Ivan Corwin, and Bálint Vető, Math. Phys. Anal. Geom. (2015), 18:20
•	KPZ universality class and the anchored Toom interface, with Gerard Barkema, Joel Lebowitz and Herbert Spohn, Phys. Rev. E 90 (2014), 042116
2013
•	Tracy-Widom asymptotics for q-TASEP, with Bálint Vető,  Ann. Inst. H. Poincaré Probab. Statist. 51 (2015), 1465-1485
•	Coupled Kardar-Parisi-Zhang equations in one dimension, with Tomohiro Sasamoto and Herbert Spohn, J. Stat. Phys. 153 (2013), 377-399
•	Scaling limit for Brownian motions with one-sided collisions, with Herbert Spohn and Thomas Weiss, Ann. Appl. Probab. 25 (2015), 1349-1382
•	Anomalous shock fluctuations in TASEP and last passage percolation models, with Peter Nejjar, Probab. Theory Relat. Fields 61 (2015), 61-109
2012
•	Perturbed GUE Minor Process and Warren’s Process with Drifts, with René Frings, J. Stat. Phys. 154 (2014), 356-377
•	On the spatial persistence for Airy processes, with René Frings, J. Stat. Mech. (2013), P02001
•	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
•	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
2011
•	Non-colliding Brownian bridges and the asymmetric tacnode process, with Bálint Vető, Electron. J. Probab. 17 (2012), no. 44, 1-17
•	Finite time corrections in KPZ growth models, with René Frings; J. Stat. Phys. 144 (2011), 1123-1150
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
•	On the partial connection between random matrices and interacting particle systems, with René Frings; J. Stat. Phys. 141 (2010), 613-637
•	Limit processes for TASEP with shocks and rarefaction fans, with Ivan Corwin and Sandrine Péché, J. Stat. Phys. 140 (2010), 232-267
•	Universality of slow decorrelation in KPZ growth, with Ivan Corwin and Sandrine Péché, Ann. Inst. H. Poincaré B 48 (2012), 134-150
2009
•	Limit process of stationary TASEP near the characteristic line, with Jinho Baik and Sandrine Péché, Comm. Pure Appl. Math 63 (2010), 1017-1070
•	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
•	Two speed TASEP, with Alexei Borodin and Tomohiro Sasamoto, J. Stat. Phys. 137 (2009), 936-977
2008
•	Airy processes with wanderers and new universality classes, with Mark Adler and Pierre Van Moerbeke, Ann. Probab. 38 (2010), 714-769
•	Anisotropic growth of random surfaces in 2+1 dimensions: fluctuations and covariance structure, with Alexei Borodin, J. Stat. Mech. (2009), P02009
•	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
•	Slow decorrelations in KPZ growth, J. Stat. Mech. (2008), P07022
•	Anisotropic growth of random surfaces in 2+1 dimensions, with Alexei Borodin, Comm. Math. Phys. 325 (2014), 603-684
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
•	Large time asymptotics of growth models on space-like paths I: PushASEP, with Alexei Borodin, Electron. J. Probab. 13 (2008), 1380-1418
•	Transition between Airy1 and Airy2 processes and TASEP fluctuations, with Alexei Borodin and Tomohiro Sasamoto, Comm. Pure Appl. Math. 61 (2008), 1603-1629
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)
•	Fluctuation properties of the TASEP with periodic initial configuration, with Alexei Borodin, Michael Prähofer and Tomohiro Sasamoto, J. Stat. Phys. 129 (2007), 1055-1080
•	Domino tilings and the six-vertex model at its free fermion point, with Herbert Spohn, J. Phys. A: Math. Gen. 39 (2006), 10297-10306
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
•	A determinantal formula for the GOE Tracy-Widom distribution, with Herbert Spohn, J. Phys. A, Math. Gen. 38 (2005), L557-L561
2004
•	Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues, Comm. Math. Phys. 252 (2004), 77-109
2003
•	Constrained Brownian motion: fluctuations away from circular and parabolic barriers, with Herbert Spohn, Ann. Probab. 33 (2005), 1302-1325
•	Fluctuations of an Atomic Ledge Bordering a Crystalline Facet, with Michael Prähofer and Herbert Spohn, Phys. Rev. E, Rapid Communications 69 (2004), 035102(R)
2002
•	Step fluctuations for a faceted crystal, with Herbert Spohn, J. Stat. Phys. 113 (2003), 1-46
•	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]
•	Last Branching in Directed Last Passage Percolation, with Herbert Spohn, Markov Process and Related Fields 9 (2003), 323-339

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
•	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.

Reviews

•	From interacting particle systems to random matrices, Contribution to StatPhys24 special issue, J. Stat. Mech. (2010), P10016
•	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
•	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

Short reviews and proceedings

•	Limit distributions for KPZ growth models with spatially homogeneous random initial conditions, in Oberwolfach Report ?? (2016), ??-??
•	Height fluctuations for the stationary KPZ equation, in Oberwolfach Report 11 (2014), 1560-1563
•	Anomalous shock fluctuations in TASEP, in Oberwolfach Report 10 (2013), 3059-3062
•	Interacting particle systems and random matrices, in Oberwolfach Report 7 (2010), 2915–2918
•	Around the universality of the Airy1 process, in Oberwolfach Report 4 (2007), 2484-2486
•	The Airy1 and Airy2 processes in the TASEP, in Oberwolfach Report 3 (2006), 2473-2476
•	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

Co-authors homepages

Other works

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