Romain Allez

PhD in Mathematics,
Post doc under the supervision of Peter K. Friz .
Visiting post-doc in Statslab, Cambridge University.

Weierstrass Institute for Applied Analysis and Stochastics (WIAS)
Mohrenstr. 39 · 10117 Berlin

E-mail: romain.allez"at"

Curriculum Vitae: click here .

PhD thesis: click here .

My main areas of expertise are probability theory and statistical physics.
My theoretical work is on random matrices, stochastic calculus, diffusion processes, statistics, Gaussian multiplicative chaos and their scale invariance properties.
I have also developed quantitative methods using random matrix tools (e.g. singular value decomposition, principal regression analysis, etc) to identify hidden patterns in noisy real-world financial data sets, including daily and intraday stock returns in financial markets.


Quantitative Finance:

Eigenvector dynamics: general theory and some applications (with J.-P. Bouchaud) Phys. Rev. E (2012).
Principal Regression Analysis and the index leverage effect (with P.-A. Reigneron and J.-P. Bouchaud) Physica A (2011).
Individual and collective stock dynamics: intra-day seasonalities (with J.-P. Bouchaud) New J. Phys. (2011).

Random matrix theory:

Rotational invariant estimator for general noisy matrices (with J. Bun, J.-P. Bouchaud, M. Potters) preprint (2015).
The eigenvectors of Gaussian matrices with an external source (with J. Bun and J.-P. Bouchaud) preprint (2015).
Random matrices in non-confining potentials (with L. Dumaz) J. Stat. Phys. in revision (2015).
From Sine Kernel to Poisson statistics (with L. Dumaz) Electron. J. Probab. (2014).
Tracy-Widom at high temperature (with L. Dumaz) J. Stat. Phys. (2014).
Eigenvector dynamics under free addition (with J.-P. Bouchaud) Random Matrices: Theory Appl. (2014).
Index Distribution of the Ginibre Ensemble (with J. Touboul and G. Wainrib) J. Phys. A: Math. Theor. (2013).
A diffusive matrix model for invariant beta-ensembles (with A. Guionnet) Electron. J. Probab. (2013).
Invariant beta-Wishart ensembles (with J.-P. Bouchaud, S. N. Majumdar and P. Vivo) J. Phys. A: Math. Theor. (2012).
Invariant beta-ensembles and the Gauss-Wigner crossover (with J.-P. Bouchaud and A. Guionnet) Phys. Rev. Lett. (2012).

Gaussian multiplicative chaos:

Lognormal scale invariant random measures (with R. Rhodes and V. Vargas) Probab. Th. Rel. Fields (2012).
Marchenko Pastur type theorem for independent MRW processes (with R. Rhodes and V. Vargas) ESAIM P&S (2011).

Links to co-authors: Jean-Philippe Bouchaud, Joël Bun, Laure Dumaz , Alice Guionnet , Satya N. Majumdar , Pierre-Alain Reigneron, Rémi Rhodes , Jonathan Touboul, Vincent Vargas , Pierpaolo Vivo , Gilles Wainrib .

Stabilité des vecteurs propres des matrices aléatoires .
Les ensembles beta invariants et l'interpolation entre Gauss et Wigner .

First explosion of the Airy diffusion: