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#### On the distribution of maximum value of the characteristic polynomial of GUE random matrices

Motivated by recently discovered relations between logarithmically correlated Gaussian processes and characteristic polynomials of large random $N \times N$ matrices $H$ from the Gaussian Unitary Ensemble (GUE), we consider ...

#### Nonlinear Analogue of the May-Wigner Instability Transition

(PNAS, 2016-01)

We study a system of $N\gg 1$ degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing ...

#### Exact solution of pulled, directed vesicles with sticky walls in two dimensions

We analyse a directed lattice vesicle model incorporating both the binding-unbinding transition and the vesicle inflation-deflation transition. From the exact solution we derive the phase diagram for this model and elucidate ...

#### Resonance width distribution in RMT: Weak coupling regime beyond Porter-Thomas

We employ the random matrix theory (RMT) framework to revisit the distribution of resonance widths in quantum chaotic systems weakly coupled to the continuum via a finite number M of open channels. In contrast to the ...

#### On Agmon metrics and exponential localization for quantum graphs

(Springer Verlag, 2018-03-28)

We investigate the rate of decrease at infinity of eigenfunctions of quantum graphs by using Agmon's method to prove $L^2$ and $L^\infty$ bounds on the product of an eigenfunction with the exponential of a certain metric. ...

#### Fluctuations in the two-dimensional one-component plasma and associated fourth-order phase transition

We study the distribution of the mean radial displacement of charges of a 2D one-component plasma in the thermodynamic limit $N\to\infty$ at finite temperature $\beta>0$. We compute explicitly the large deviation functions ...