59 research outputs found
Complex Langevin Dynamics for chiral Random Matrix Theory
We apply complex Langevin dynamics to chiral random matrix theory at nonzero
chemical potential. At large quark mass the simulations agree with the
analytical results while incorrect convergence is found for small quark masses.
The region of quark masses for which the complex Langevin dynamics converges
incorrectly is identified as the region where the fermion determinant
frequently traces out a path surrounding the origin of the complex plane during
the Langevin flow. This links the incorrect convergence to an ambiguity in the
Langevin force due to the presence of the logarithm of the fermion determinant
in the action.Comment: 23 pages, 10 figure
Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
It is demonstrated that the complex Langevin method can simulate chiral
random matrix theory at non-zero chemical potential. The successful match with
the analytic prediction for the chiral condensate is established through a
shift of matrix integration variables and choosing a polar representation for
the new matrix elements before complexification. Furthermore, we test the
proposal to work with a Langevin-time dependent quark mass and find that it
allows us to control the fluctuations of the phase of the fermion determinant
throughout the Langevin trajectory.Comment: 16 pages, 6 figure
Bailouts in a common market: a strategic approach
Governments in the EU grant Rescue and Restructure Subsidies to bail out ailing firms. In an international asymmetric Cournot duopoly we study effects of such subsidies on market structure and welfare. We adopt a common market setting, where consumers from the two countries form one market. We show that the subsidy is positive also when it fails to prevent the exit. The reason is a strategic effect, which forces the more efficient firm to make additional cost-reducing effort. When the exit is prevented, allocative and productive efficiencies are lower and the only gaining player is the rescued firm
Understanding the interplay between social and spatial behaviour
According to personality psychology, personality traits determine many aspects of human behaviour. However, validating this insight in large groups has been challenging so far, due to the scarcity of multi-channel data. Here, we focus on the relationship between mobility and social behaviour by analysing trajectories and mobile phone interactions of ∼1000 individuals from two high-resolution longitudinal datasets. We identify a connection between the way in which individuals explore new resources and exploit known assets in the social and spatial spheres. We show that different individuals balance the exploration-exploitation trade-off in different ways and we explain part of the variability in the data by the big five personality traits. We point out that, in both realms, extraversion correlates with the attitude towards exploration and routine diversity, while neuroticism and openness account for the tendency to evolve routine over long time-scales. We find no evidence for the existence of classes of individuals across the spatio-social domains. Our results bridge the fields of human geography, sociology and personality psychology and can help improve current models of mobility and tie formation
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