Search
Now showing items 1-4 of 4
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 ...
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 ...
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 ...
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 ...