Prof. Dr. Ashkan Nikeghbali
Institut für Mathematik
Universität Zürich
Winterthurerstrasse 190
CH-8057 Zürich
E-Mail:
Office: Y27K10
Universität Zürich
Winterthurerstrasse 190
CH-8057 Zürich
E-Mail:
Office: Y27K10
Field of Research:
Finanzmathematik
Stochastische Prozesse
Zahlentheorie
Stochastische Prozesse
Zahlentheorie
Working group:
Secretary:
E-Mail:
Phone:
E-Mail:
Phone:
Chair in Probability Theory
My research interests include:
Random matrix theory
- Study of the classical groups, eigenvalues asymptotics, distribution of the characteristic polynomial and ratios;
- Orthogonal polynomials on the unit circle;
- Random operators associated to random matrices.
Mod-phi convergence and limit theorems for dependent random variables
- Weak convergence, distributional approximations, rate of convergence;
- Normality zones;
- Precise moderate and large deviations;
- Applications to combinatorics, random graphs, random permutations, statistical mechanics, sums of weakly dependent random variables, random matrix theory, mathematical finance.
Analytic number theory
- Distribution of values of L-functions, density problems, limit theorems for L-functions, random matrix models and prediction in number theory;
- Random multiplicative functions.
- Mathematical Finance
- Loss portfolios, modeling dependence;
- Applications of the theory of enlargements of filtrations and random times to mathematical finance.
Other professional activity:
I am a strategy advisor at Roche for stochastic modeling and data analytics, from October 2020.
Since 2016 I have been a member of the Scientific Advisory Board of swissQuant and a member of the Advisory Board of EVMTech.
I was awarded an Honorary Doctorate from the "1 Decembrie 1918" University of Alba Iulia.
Publications
.
Preprints Submitted
Ashkan Nikeghbali, Pierre-Loic Méliot, Gabriele Visentin (2022). Mod-Poisson approximation schemes: applications to credit risk. Preprint [pdf]
Ashkan Nikeghbali, Pierre-Loic Méliot, Gabriele Visentin (2022). Mod-Poisson approximation schemes and higher order Chen-Stein inequalities. Preprint [pdf]
Ashkan Nikeghbali, Pierre-Loic Méliot (2022). Asymptotics of the major index of a random standard tableau . Preprint [pdf]
Ashkan Nikeghbali, Pierre-Loic Méliot (2022). Gaussian approximations for random vectors. Preprint. [pdf]
Ashkan Nikeghbali, Gabriele Visentin, Giuseppe Genovese, Nicola Serra (2022). Universal approximation of credit portfolio using restricted Boltzmann machines. Preprint. [pdf]
Ashkan Nikeghbali, Pierre-Loic Méliot (2022). On the precise deviations of the characteristic polynomial of a random matrix. Preprint. [pdf]
Ashkan Nikeghbali, Joseph Najnudel (2022). Convergence of random holomorphic functions with real zeros and extensions of the stochastic zeta function. Preprint. [pdf]
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Published / Accepted
Ashkan Nikeghbali, Pierre-Loic Méliot, Valentin Féray (2017). Graphons, Permutons and the Thoma simplex: three mod-Gaussian moduli spaces. To appear in the Proceedings of the London Mathematical Society. [pdf]
Ashkan Nikeghbali, Reda Chhaibi, Freddy Delbaen, Pierre-Loic Méliot (2016). Mod-phi convergence, IV: Approximation of discrete measures and harmonic analysis on the torus. To appear in Annales de l'Institut Fourier [pdf]
Ashkan Nikeghbali, Reda Chhaibi, Joseph Najnudel, Bradley William Rodgers, Emma Hovhannisyan (2019). The limiting characteristic polynomial of classical random matrix ensembles. To appear In Annales de l'IHP. [pdf]
Ashkan Nikeghbali, Martina Dal Borgo, Pierre-Loic Méliot (2019). Local Limit Theorems and mod-phi convergence. To appear in ALEA. [pdf]
Kenneth Maples, Joseph Najnudel, Ashkan Nikeghbali (2013). Limit operators for circular ensembles. To appear in Annals of Probability. [pdf]
Ashkan Nikeghbali, Pierre-Loic Méliot, Valentin Féray (2016). Mod-phi convergence, II: Estimates of the speed of convergence . To appear in Séminaire des Probabilités [pdf]
Reda Chhaibi, Joseph Najnudel, Ashkan Nikeghbali. The Circular Unitary Ensemble and the Riemann Zeta Function: the microscopic landscape and a new approach to ratios. Invent. Math. 207, no. 1, 23--113 (2017) [pdf]
Valentin Féray, Pierre-Loic Méliot, Ashkan Nikeghbali (2016). Mod- phi convergence: Normality zones and precise deviations. SprigerBriefs in Probability and Mathematical Statistics [pdf]
Pierre-Loic Méliot, Ashkan Nikeghbali (2015). Mod-Gaussian convergence and its applications for models of statistical mechanics. In memoriam Marc Yor—Séminaire de Probabilités XLVII, 369--425, Lecture Notes in Math., 2137, Springer (2015). [pdf]
Emmanuel Kowalski, Joseph Najnudel, Ashkan Nikeghbali (2015). A characterization of limiting functions arising in mod-* convergence. Electron. Commun. Probab. 20, no. 70, 1--11 (2015). [pdf]
Adam Harper, Ashkan Nikeghbali, Maksym Radziwill (2015). A note on Helson’s conjecture on moments of random multiplicative functions. Analytic Number Theory, Springer, 145--169 (2015). [pdf]
Yacine Barhoumi, Christopher Hughes, Joseph Najnudel, Ashkan Nikeghbali (2013). On the number of zeros of linear combinations of independent characteristic polynomials of random unitary matrices. Int. Math. Res. Not. IMRN, no. 23, 12366--12404 (2015). [pdf]
Dörte Kreher, Ashkan Nikeghbali (2015). A new kind of augmentation of filtrations suitable for a change of probability measure by a strict local martingale. Statist. Probabilist. Lett., 104, 94--101 (2015). [pdf]
Joseph Najnudel, Ashkan Nikeghbali, Alain Rouault (2014). Limit theorems for orthogonal polynomials related to circular ensembles. J. Theoret. Probab. 29, 145--169 (2016) [pdf]
Constantinos Kardaras, Dörte Kreher, Ashkan Nikeghbali (2011). Strict local martingales and bubbles. Ann. Appl. Probab. 25, no.4, 1827--1867 (2015). [pdf]
Freddy Delbaen, Emmanuel Kowalski, Ashkan Nikeghbali. Mod-phi convergence. Int. Math. Res. Not. IMRN, no.11, 3445--3485 (2015). [pdf]
Joseph Najnudel, Ashkan Nikeghbali (2014). On a flow of operators associated to virtual permutations. Séminaire de Probabilités XLVI, Lecture Notes in Math., 2123, Springer, 481--512 (2014). [pdf]
Christopher Hughes, Joseph Najnudel, Ashkan Nikeghbali, Dirk Zeindler (2011). Random permutation matrices under the generalized Ewens measure . Annals of Applied Probability, Vol. 23(3), 987-1024 (2013) [pdf]
Ashkan Nikeghbali, Eckhard Platen (2012). A reading guide for last passage times with financial applications in view. Finance and Stochastics, Vol. 17(3), 615-640 (2013) [pdf]
Ashkan Nikeghbali, Dirk Zeindler (2012). The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles. Ann. Inst. Henri Poincaré Probab. Stat. 49 (2013), no. 4, 961-981 [pdf]
Kenneth Maples, Ashkan Nikeghbali, Dirk Zeindler (2012). On the number of cycles in a random permutation. Electronic Communications in Probability, 17, no. 20, 1-13 (2012) [pdf]
Paul Bourgade, Joseph Najnudel, Ashkan Nikeghbali (2013). A unitary extension of virtual permutations. International Mathematics Research Notices, 2013(18):4101-4134 [pdf]
Joseph Najnudel, Ashkan Nikeghbali. The distribution of eigenvalues of randomized permutation matrices. Annales de l'institut Fourier, 63 no. 3 (2013), p. 773-838 [pdf]
Ashkan Nikeghbali, Joseph Najnudel (2009). A new construction of the $\sigma$-finite measures associated with submartingales of class $(\Sigma)$. C. R. Math. Acad. Sci. Paris, Volume 348, pp. 311-316, (2010) [pdf]
Ashkan Nikeghbali, Emmanuel Kowalski (2012). Mod-Gaussian convergence and the value distribution of zeta(1/2+it) and related quantities. Journal of the London Mathematical Society (2), 86, no. 1, 291-319 (2012) [pdf]
Andrew Barbour, Emmanuel Kowalski, Ashkan Nikeghbali (2013). Mod-discrete expansions. Probab. Theory and Related Fields, 158, no. 3-4, 859--893 (2014). [pdf]
Ashkan Nikeghbali, Joseph Najnudel (2010). A remarkable sigma-finite measure associated with last passage times and penalisation results. Contemporary Quantitative Finance, Essays in Honour of Eckhard Platen, pp. 77-98, Springer (2010) [pdf]
Ashkan Nikeghbali, Joseph Najnudel (2009). On some properties of a universal sigma finite measure associated with a remarkable class of submartingales. Publ. of the Res. Instit. for Math. Sci. (Kyoto University), 47 (2011), no. 4, 911-936 [pdf]
Ashkan Nikeghbali, Joseph Najnudel. On penalization results related with a remarkable class of submartingales. Markov process. Related Fields, 19, no.4, 763--790 (2013) [pdf]
Ashkan Nikeghbali, Joseph Najnudel (2009). A new kind of augmentation of filtrations. ESAIM, 15, pp. 39-57, (2011) [pdf]
Ashkan Nikeghbali, Patrick Cheridito, Eckhard Platen (2012). Processes of class sigma, last passage times, and drawdowns. SIAM Journal on Financial Mathematics, 3(2012), no. 1, 280-303 [pdf]
Ashkan Nikeghbali, Joseph Najnudel (2009). On some universal sigma-finite measures and some extensions of Doob's optional stopping theorem. Stochastic Process. Appl., 122, no.4, 1582--1600 (2012). [pdf]
Ashkan Nikeghbali, Emmanuel Kowalski (2009). Mod-Poisson convergence in probability and number theory. Intern. Math. Res. Not., 18, pp. 3549-3587, (2010). [pdf]
Ashkan Nikeghbali, Joseph Najnudel, Felix Rubin (2009). Scaled limit and rate of convergence for the largest eigenvalue from the generalized Cauchy random matrix ensemble. Journal of Statistical Physics, Volume 137, no. 2, pp. 373-406, (2009)
Ashkan Nikeghbali, Jean Jacod, Emmanuel Kowalski (2008). Mod-Gaussian convergence: new limit theorems in Probability and Number Theory. Forum Mathematicum, Vol. 23, No. 4, pp. 835-873, (2011) [pdf]
Ashkan Nikeghbali, Delia Marina Coculescu, Monique Jeanblanc (2008). Default times, non arbitrage conditions and change of probability measures. Finance and Stochastics, 16(2012), no. 3, 513-535 [pdf]
Ashkan Nikeghbali, Delia Marina Coculescu (2008). Hazard processes and martingale hazard processes. Mathematical Finance 22(2012), no. 3, 519-537 [pdf]
Ashkan Nikeghbali, Paul Bourgade, Alain Rouault (2009). Ewens measures on compact groups and hypergeometric kernels. Séminaires de Probabilités, Vol. 43, pp. 351-377, LNM 2006 (2011) [pdf]
Ashkan Nikeghbali, Paul Bourgade, Alain Rouault (2008). Circular Jacobi ensemble and deformed Verblunsky coefficients. IMRN, Vol. 2009, No. 23, pp. 4357-4394 [pdf]
Ashkan Nikeghbali, Marc Yor (2008). The Barnes G function and its relations with sums and products of generalized Gamma . Elect. Comm. in Probab. 14, 396–411, (2009) [pdf]
Ashkan Nikeghbali, Delia Marina Coculescu (2007). Filtrations. Encyclopedia of Quantitative Finance, Wiley, vol. II, pp. 683-686, (2010) [pdf]
Ashkan Nikeghbali, Christopher Hughes, Paul Bourgade, Marc Yor (2008). The characteristic polynomial of a random unitary matrix: a probabilistic approach.. Duke Math. J., 145, pp. 45-69, (2008) [pdf]
Ashkan Nikeghbali, Christopher Hughes (2008). Zeros of random polynomials cluster uniformly near the unit circle. Compositio Mathematica, vol. 144, Part 3, pp. 734-746 (2008) [pdf]
Ashkan Nikeghbali, Christopher Hughes, Marc Yor (2008). An arithmetic model for the total disorder process. Probab. Theory and Related Fields, 141, no. 1-2, pp. 47-59, (2008) [pdf]
Ashkan Nikeghbali (2008). How badly are the Burholder-Davis-Gundy inequalities affected by arbitrary random times?. Statistics and Probability Letters, vol. 78, Issue 6, pp. 766-770, (2008) [pdf]
Ashkan Nikeghbali, Paul Bourgade, Alain Rouault (2007). The characteristic polynomial on compact groups with Haar measure: some equalities in law.. C. R. Acad. Sci. Paris, Ser. I, 345, no. 4, pp. 229-232, (2007) [pdf]
Ashkan Nikeghbali (2007). Non stopping times and stopping theorems. Stochastic Process. Appl. 117, no. 4, pp. 457-475, (2007) [pdf]
Ashkan Nikeghbali (2006). Enlargements of filtrations and path decompositions at non stopping times. Probab. Theory and Related Fields, 136, no. 4, pp. 524-540, (2006) [pdf]
Ashkan Nikeghbali, Marc Yor (2006). Doob's maximal identity, multiplicative decompositions and enlargements of filtrations. Illinois Journal of Mathematics, 50, no. 1-4, pp. 791-814, (2006) [pdf]
Ashkan Nikeghbali. Multiplicative decompositions and frequency of vanishing of nonnegative submartingales. J. Theoret. Probab. 19 , no. 4, pp. 931-949, (2006) [pdf]
Ashkan Nikeghbali. A class of remarkable submartingales. Stochastic Process. Appli. 116, no. 6, pp. 917-938 (2006) [pdf]
Ashkan Nikeghbali (2006). Some random times and martingales associated with $BES_0(\delta)$ processes ($0<\delta<2$). ALEA Lat. Am. J. Probab. Math. Stat. 2, pp. 67-89 (2006) [pdf]
Ashkan Nikeghbali (2006). An essay on the general theory of stochastic processes. Probab. Surv. 3, pp. 345-412, (2006) [pdf]
Ashkan Nikeghbali, Marc Yor (2005). A definition and some characteristic properties of pseudo-stopping times. Annals of Probability, Vol. 33, No. 5, pp. 1804-1824, (2005) [pdf]
Ashkan Nikeghbali (2005). "Temps aleatoires, filtrations, sous-martingales: quelques developpements recents.". Ph.D in mathematics supervised by Marc Yor: Universite Pierre et Marie Curie, Paris 6 (2005).
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Guest
| 2026 | 2025 | 2024 | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | All |
| Guest | Stay | |
| Prof. Dr. Jürgen Angst, Université de Rennes 1 (Rennes) | 03.12.17 - 05.12.17 | Nikeghbali, Ashkan |
| Prof. Dr. Philippe Bougerol, Université Pierre et Marie Curie Paris 6 (Paris) | 31.10.17 - 01.11.17 | Nikeghbali, Ashkan |
| Prof. Dr. Manon Defosseux, Université René Descartes Paris 5 (Paris) | 31.10.17 - 01.11.17 | Nikeghbali, Ashkan |
| Prof. Dr. Thomas Dreyfus, Université Claude Bernard Lyon 1 (Lyon) | 31.10.17 - 01.11.17 | Nikeghbali, Ashkan |
| Prof. Dr. Vladimir Fock, Université de Strasbourg (Strasbourg) | 31.10.17 - 01.11.17 | Nikeghbali, Ashkan |
| Dr. Thierry Lévy, Université Pierre et Marie Curie Paris 6 (Paris) | 31.10.17 - 01.11.17 | Nikeghbali, Ashkan |
| Dr. Pierre-Loic Méliot, Département de Mathématiques, Université d'Orsay (Orsay, FR) | 31.10.17 - 03.11.17 | Nikeghbali, Ashkan |
| Prof. Dr. Neil O'Connell, University College Dublin (Dublin) | 31.10.17 - 01.11.17 | Nikeghbali, Ashkan |
| Prof. Dr. Jean-François Quint, CNRS - Université de Bordeaux (Talence Cedex, France) | 31.10.17 - 01.11.17 | Nikeghbali, Ashkan |
| Prof. Dr. Alexey Bufetov, Institute for Applied Mathematics, Universität Bonn (Bonn, Deutschland) | 30.10.17 - 11.11.17 | Nikeghbali, Ashkan |
| Dr. Dirk Zeindler, School of Mathematical Sciences, Lancaster University (Lancaster) | 30.10.17 - 02.11.17 | Nikeghbali, Ashkan |
| Prof. Dr. Catherine Donati-Martin, Université Versailles St Quentin (Versailles) | 26.09.17 - 27.09.17 | Nikeghbali, Ashkan |
| Prof. Dr. Alain Rouault, LMV UMR, Université de Versailles-Saint-Quentin (Versailles) | 25.09.17 - 27.09.17 | Nikeghbali, Ashkan |
| Prof. Dr. Joseph Najnudel, University of Bristol (Bristol, UK) | 23.09.17 - 28.09.17 | Nikeghbali, Ashkan |
| Dr. Dirk Zeindler, School of Mathematical Sciences, Lancaster University (Lancaster) | 24.07.17 - 30.08.17 | Nikeghbali, Ashkan |
| Prof. Dr. Joseph Najnudel, University of Bristol (Bristol, UK) | 18.07.17 - 21.07.17 | Nikeghbali, Ashkan |
| Prof. Dr. Alain Rouault, LMV UMR, Université de Versailles-Saint-Quentin (Versailles) | 11.01.17 - 13.01.17 | Nikeghbali, Ashkan |
| Dr. Adrian Röllin, National University of Singapore (Singapore) | 21.10.16 - 12.01.17 | Nikeghbali, Ashkan |
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Events
The Secret of Life Research Camp
November 22 - 26, 2021, in Zurich
8th Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
November 28 - 29, 2019, in Zurich
7th Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
October 25 - 26, 2018, in Strasbourg
Random geometries / Random topologies
December 4 - 5, 2017, at ETH Zürich, in Zurich
6th Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
October 31 - November 1, 2017, in Zurich
5th Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
March 23 - 24, 2017, in Strasbourg
4th Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
November 3 - 4, 2016, in Zurich
Enlargements of Filtrations and Financial Applications
May 2 - 3, 2016, in Évry
September 8 - 9, 2016, in Zurich
50th Swiss Probability Seminar
June 6 - 7, 2016, in Zurich
3rd Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
March 4 - 5, 2016, in Strasbourg
2nd Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability
October 29 - 30, 2015, in Zurich
1st Strasbourg / Zurich - Meeting: Frontiers in Analysis and Probability, February 19 - 20, 2015, in Strasbourg
Swiss Probability Seminar
Workshop on Mathematics in Finance, October 18, 2013
Workshop on Lévy processes and their applications, December 13 - 14, 2010
Workshop on Random Matrices, April 15 - 16, 2010
From October 27 - 31, 2008, Emmanuel Kowalski and myself organized the conference
"Random Matrices, L- Functions and Primes" at ETH Zürich,
sponsored by the Forschungsinstitut für Mathematik
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