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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 ...
Critical Gagliardo-Nirenberg, Trudinger, Brezis-Gallouet-Wainger inequalities on graded groups and ground states
In this paper we investigate critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities associated with the positive Rockland operators on graded groups, which includes the cases of $\mathbb R^n$, ...
Hardy inequalities on metric measure spaces, II: The case $p>q$
In this note we continue giving the characterisation of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on ...
Counting equilibria of large complex systems by instability index
We consider a nonlinear autonomous system of $N\gg 1$ degrees of freedom randomly coupled by both relaxational ('gradient') and non-relaxational ('solenoidal') random interactions. We show that with increased interaction ...
Direct and Inverse problems for time-fractional pseudo-parabolic equations
The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. We are especially interested in proving ...
