Rivalry, Exclusion and Coalitions

Coalition formation, exclusion contest, tragedy of the commons

Application of Portfolio Management Theory: Managing the US Air Force Acquisition Portfolio

Student research poste

Chez Hans A La Carte Menu 2017

Fine dining restaurant in a converted Victorian Gothic church, with a daily changing European menu.https://arrow.tudublin.ie/menus21c/1328/thumbnail.jp

Chez Hans A La Carte Dessert Menu 2017

Fine dining restaurant in a converted Victorian Gothic church, with a daily changing European menu.https://arrow.tudublin.ie/menus21c/1327/thumbnail.jp

Chez Hans Dessert Menu 2017

Fine dining restaurant in a converted Victorian Gothic church, with a daily changing European menu.https://arrow.tudublin.ie/menus21c/1329/thumbnail.jp

Chez Hans Weekday Menu 2017

Fine dining restaurant in a converted Victorian Gothic church, with a daily changing European menu.https://arrow.tudublin.ie/menus21c/1331/thumbnail.jp

Chez Hans Group Menu 2017

Fine dining restaurant in a converted Victorian Gothic church, with a daily changing European menu.https://arrow.tudublin.ie/menus21c/1330/thumbnail.jp

Entanglement Entropy and Full Counting Statistics for 2d2d-Rotating Trapped Fermions

We consider $N$ non-interacting fermions in a $2d$ harmonic potential of trapping frequency $\omega$ and in a rotating frame at angular frequency $\Omega$, with $0<\omega - \Omega\ll \omega$. At zero temperature, the fermions are in the non-degenerate lowest Landau level and their positions are in one to one correspondence with the eigenvalues of an $N\times N$ complex Ginibre matrix. For large $N$, the fermion density is uniform over the disk of radius $\sqrt{N}$ centered at the origin and vanishes outside this disk. We compute exactly, for any finite $N$, the R\'enyi entanglement entropy of order $q$, $S_q(N,r)$, as well as the cumulants of order $p$, $\langle{N_r^{p}}\rangle_c$, of the number of fermions $N_r$ in a disk of radius $r$ centered at the origin. For $N \gg 1$, in the (extended) bulk, i.e., for $0 < r/\sqrt{N} < 1$, we show that $S_q(N,r)$ is proportional to the number variance ${\rm Var}\,(N_r)$, despite the non-Gaussian fluctuations of $N_r$. This relation breaks down at the edge of the fermion density, for $r \approx \sqrt{N}$, where we show analytically that $S_q(N,r)$ and ${\rm Var}\,(N_r)$ have a different $r$-dependence.Comment: 6 pages + 7 pages (Supplementary material), 2 Figure

Extremes of 2d2d Coulomb gas: universal intermediate deviation regime

In this paper, we study the extreme statistics in the complex Ginibre ensemble of $N \times N$ random matrices with complex Gaussian entries, but with no other symmetries. All the $N$ eigenvalues are complex random variables and their joint distribution can be interpreted as a $2d$ Coulomb gas with a logarithmic repulsion between any pair of particles and in presence of a confining harmonic potential $v(r) \propto r^2$. We study the statistics of the eigenvalue with the largest modulus $r_{\max}$ in the complex plane. The typical and large fluctuations of $r_{\max}$ around its mean had been studied before, and they match smoothly to the right of the mean. However, it remained a puzzle to understand why the large and typical fluctuations to the left of the mean did not match. In this paper, we show that there is indeed an intermediate fluctuation regime that interpolates smoothly between the large and the typical fluctuations to the left of the mean. Moreover, we compute explicitly this "intermediate deviation function" (IDF) and show that it is universal, i.e. independent of the confining potential $v(r)$ as long as it is spherically symmetric and increases faster than $\ln r^2$ for large $r$ with an unbounded support. If the confining potential $v(r)$ has a finite support, i.e. becomes infinite beyond a finite radius, we show via explicit computation that the corresponding IDF is different. Interestingly, in the borderline case where the confining potential grows very slowly as $v(r) \sim \ln r^2$ for $r \gg 1$ with an unbounded support, the intermediate regime disappears and there is a smooth matching between the central part and the left large deviation regime.Comment: 36 pages, 7 figure