63,562 research outputs found
N=2 supersymmetric QCD and elliptic potentials
We investigate the relation between the four dimensional N=2 SU(2) super
Yang-Mills theory with four fundamental flavors and the quantum mechanics model
with Treibich-Verdier potential described by the Heun equation in the elliptic
form. We study the precise correspondence of quantities in the gauge theory and
the quantum mechanics model. An iterative method is used to obtain the
asymptotic expansion of the spectrum for the Schr\"{o}dinger operator, we are
able to fix the precise relation between the energy spectrum and the instanton
partition function of the gauge theory. We also study asymptotic expansions for
the spectrum which correspond to the strong coupling regions of the
Seiberg-Witten theory.Comment: Latex, 29pp, published version, content restructured and simplifie
Rejoinder: Conditional Growth Charts
Rejoinder: Conditional Growth Charts [math.ST/0702634]Comment: Published at http://dx.doi.org/10.1214/009053606000000678 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Dynamic Games with Almost Perfect Information
This paper aims to solve two fundamental problems on finite or infinite
horizon dynamic games with perfect or almost perfect information. Under some
mild conditions, we prove (1) the existence of subgame-perfect equilibria in
general dynamic games with almost perfect information, and (2) the existence of
pure-strategy subgame-perfect equilibria in perfect-information dynamic games
with uncertainty. Our results go beyond previous works on continuous dynamic
games in the sense that public randomization and the continuity requirement on
the state variables are not needed. As an illustrative application, a dynamic
stochastic oligopoly market with intertemporally dependent payoffs is
considered
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