Metal-Insulator Transition of the Quasi-One Dimensional Luttinger Liquid Due to the Long-Range Character of the Coulomb Interaction

An instability of the quasi-1D Luttinger liquid associated with the metal - insulator transition is considered. The homogeneous metal ground state of this liquid is demonstrated to be unstable and the charge-density wave arises in the system. The wavevector of this wave has nonzero component both along the direction of the chains and in the perpendicular direction. The ground state of the system has a dielectric gap at the Fermi surface, the value of this gap being calculated.Comment: RevTex, 10 page

Query Complexity of Approximate Nash Equilibria

We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players $n$. Our main result states that for $n$-player binary-action games and for constant $\varepsilon$, the query complexity of an $\varepsilon$-well-supported Nash equilibrium is exponential in $n$. One of the consequences of this result is an exponential lower bound on the rate of convergence of adaptive dynamics to approxiamte Nash equilibrium

Excitonic Instability and Origin of the Mid-Gap States

In the framework of the two-band model of a doped semiconductor the self-consistent equations describing the transition into the excitonic insulator state are obtained for the 2D case. It is found that due to the exciton-electron interactions the excitonic phase may arise with doping in a semiconductor stable initially with respect to excitonic transition in the absence of doping. The effects of the strong interactions between electron (hole) Fermi-liquid (FL) and excitonic subsystems can lead to the appearance of the states lying in the middle of the insulating gap.Comment: 2 pages with 2 figures available upon request, LaTex Version 3.0 (PCTeX), to appear in the Proceedings of the M2S-HTSC IV Conferenc

Graphical potential games

We study the class of potential games that are also graphical games with respect to a given graph $G$ of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of Markov random fields on $G$. From this characterization, and from the Hammersley-Clifford theorem, it follows that the potentials of such games can be decomposed to local potentials. We use this decomposition to strongly bound the number of strategy changes of a single player along a better response path. This result extends to generalized graphical potential games, which are played on infinite graphs.Comment: Accepted to the Journal of Economic Theor

Query Complexity of Correlated Equilibrium

We study lower bounds on the query complexity of determining correlated equilibrium. In particular, we consider a query model in which an n-player game is specified via a black box that returns players' utilities at pure action profiles. In this model we establish that in order to compute a correlated equilibrium any deterministic algorithm must query the black box an exponential (in n) number of times.Comment: Added reference

Approximate Nash Equilibria via Sampling

We prove that in a normal form n-player game with m actions for each player, there exists an approximate Nash equilibrium where each player randomizes uniformly among a set of O(log(m) + log(n)) pure strategies. This result induces an $N^{\log \log N}$ algorithm for computing an approximate Nash equilibrium in games where the number of actions is polynomial in the number of players (m=poly(n)), where $N=nm^n$ is the size of the game (the input size). In addition, we establish an inverse connection between the entropy of Nash equilibria in the game, and the time it takes to find such an approximate Nash equilibrium using the random sampling algorithm

On boundary fusion and functional relations in the Baxterized affine Hecke algebra

We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain models. We show that these operators lead to a family of commuting transfer matrices of Sklyanin type. We derive fusion type functional relations for these operators for two families of representations.Comment: 35 pages, 3 figure