# Nicholas Simm

## Dr Nicholas SimmResearch Fellow |

**Teaching responsibilities 2017/18:**

MA901 Fundamental Tools (Shared with statistics.)

I am a Leverhulme Early Career Fellow at the Mathematics Institute, University of Warwick.

I work on mathematical physics and probability - specifically on the theory and applications of random matrices (RMT). I am interested in the issue of Gaussian fluctuations in RMT and its relation to the Gaussian free field or other `log-correlated' stochastic processes. (pre-print 1, publications 3, 5 and 7 below).

My thesis topic concerned the random matrix approach to quantum systems with a chaotic classical limit, mainly on transport properties in these systems and the relation to orthogonal polynomials, integrable hierarchies and Painlevé equations (see publications 9, 10, 11). This is a topic I continue to work on with my collaborators (publications 4 and 6).

Finally, I have worked on `fundamental problems' in RMT - such as `How many eigenvalues of a large random matrix are real (publication 1) and what is the probability distribution of this number?' (publication 3) or 'What is the probability that a random Hermitian matrix is positive definite?' (publication 2).

**Pre-prints**

- "Subcritical multiplicative chaos for regularized counting statistics from random matrix theory" (with G. Lambert and D. Ostrovsky) arXiv:1612.02367 (submitted).

**Published papers**

- "On the real spectrum of a product of Gaussian random matrices"
*Electronic Communications in Probability***22**, no. 41 (11pp), 2017. (arXiv:1701.09176) - "On the probability of positive-definiteness in the gGUE via semi-classical Laguerre polynomials" (with A. Deaño).
*Journal of Approximation Theory***220**, 44-59, 2017. (arXiv:1610.08561) - "Central limit theorems for the real eigenvalues of large Gaussian random matrices".
*Random Matrices: Theory and Applications***06**, 1750002, 2017. (arXiv:1512.01449) - “Large-N expansion for the time-delay matrix of ballistic chaotic cavities” (with F. D. Cunden, F. Mezzadri and P. Vivo).
*Journal of Mathematical Physics***57**, 111901, 2016. (arXiv:1607.00250) -
“Fractional Brownian Motion with Hurst Index H=0 and the Gaussian Unitary Ensemble” (with Y. V. Fyodorov and B. A. Khoruzhenko).

*Annals of Probability***44**, 4, 2980-3031, 2016. (arXiv:1312.0212) -
“Correlators for the Wigner-Smith time-delay matrix of chaotic cavities” (with F. D. Cunden, F. Mezzadri and P. Vivo).

*Journal of Physics A: Mathematical and Theoretical***49**, 18LT01, 2016. (arXiv:1601.06690) - “On the distribution of the maximum value of the characteristic polynomial of GUE random matrices” (with Y. V. Fyodorov).
*Nonlinearity***29**, 9, 2016. (arXiv:1503.07110) - “Energy landscape of the finite-size mean-field 2-spin spherical model and topology trivialization” (with D. Mehta, J. D. Hauenstein, M. Niemerg and D. A. Stariolo).
*Physical Review E.***91**, 022133 2015. (arXiv:1409.8303) - “Tau-Function Theory of Quantum Chaotic Transport with beta = 1,2,4” (with F. Mezzadri).
*Communications in Mathematical Physics***324**, 465-513, 2013. (arXiv:1206.4584) - “Moments of the transmission eigenvalues, proper delay times, and random matrix theory II” (with F. Mezzadri).
*Journal of Mathematical Physics***53**053504, 2012. (arXiv:1108.2859) - “Moments of the transmission eigenvalues, proper delay times, and random matrix theory I” (with F. Mezzadri).
*Journal of Mathematical Physics***52**103511, 2011. (arXiv:1103.6203)

**Teaching Responsibilities 2015/16:**

Term 2: MA254 Theory of ODEs