4,960 research outputs found
Effects of disorder on conductance through small interacting systems
We study the effects of disorders on the transport through small interacting
systems based on a two-dimensional Hubbard cluster of finite size connected to
two noninteracting leads. This system can be regarded as a model for the
superlattice of quantum dots or atomic network of the nanometer size.
We calculate the conductance at T=0 using the order self-energy in an
electron-hole symmetric case. The results show that the conductance is ensitive
to the randomness when the resonance states are situated near the Fermi energy.Comment: 2 pages, 3 figures, to be published in Physica E, proceedings Low
Temperature Physics 23 (Hirosima, Japan
Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis
The maximum entropy principle is a powerful tool for solving underdetermined
inverse problems. This paper considers the problem of discretizing a continuous
distribution, which arises in various applied fields. We obtain the
approximating distribution by minimizing the Kullback-Leibler information
(relative entropy) of the unknown discrete distribution relative to an initial
discretization based on a quadrature formula subject to some moment
constraints. We study the theoretical error bound and the convergence of this
approximation method as the number of discrete points increases. We prove that
(i) the theoretical error bound of the approximate expectation of any bounded
continuous function has at most the same order as the quadrature formula we
start with, and (ii) the approximate discrete distribution weakly converges to
the given continuous distribution. Moreover, we present some numerical examples
that show the advantage of the method and apply to numerically solving an
optimal portfolio problem.Comment: 20 pages, 14 figure
Computational Complexity in the Design of Voting Rules
This paper discusses an aspect of computational complexity in social choice theory. We consider the problem of designing voting rules, which is formulated in terms of simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not.
Mutual Knowledge of Rationality in the Electronic Mail Game
This paper reexamines the paradoxical aspect of the electronic mail game (Rubinstein, 1989). The electronic mail game is a coordination game with payoff uncertainty. At a Bayesian Nash equilibrium of the game, players cannot achieve the desired coordination of actions even when a high order of mutual knowledge of payoff functions obtains. We want to make explicit the role of knowledge about rationality of players, not only that of payoff functions. For this purpose, we use an extended version of the belief system model developed by Aumann and Brandenburger (1995). We propose a certain way of embedding the electronic mail game in an belief system. And we show that for rational players to coordinate their actions, for any embedding belief systems, it is necessary that the upper bound order of mutual knowledge of payoff functions exceeds the upper bound order of mutual knowledge of rationality. This result implies that under common knowledge of rationality, the coordination never occurs, which is similar to Rubinstein's result. We point out, however, that there exists a class embedding belief systems for which the above condition is also sufficient for the desired coordination.
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