45,086 research outputs found
Self-stabilizing uncoupled dynamics
Dynamics in a distributed system are self-stabilizing if they are guaranteed
to reach a stable state regardless of how the system is initialized. Game
dynamics are uncoupled if each player's behavior is independent of the other
players' preferences. Recognizing an equilibrium in this setting is a
distributed computational task. Self-stabilizing uncoupled dynamics, then, have
both resilience to arbitrary initial states and distribution of knowledge. We
study these dynamics by analyzing their behavior in a bounded-recall
synchronous environment. We determine, for every "size" of game, the minimum
number of periods of play that stochastic (randomized) players must recall in
order for uncoupled dynamics to be self-stabilizing. We also do this for the
special case when the game is guaranteed to have unique best replies. For
deterministic players, we demonstrate two self-stabilizing uncoupled protocols.
One applies to all games and uses three steps of recall. The other uses two
steps of recall and applies to games where each player has at least four
available actions. For uncoupled deterministic players, we prove that a single
step of recall is insufficient to achieve self-stabilization, regardless of the
number of available actions
Hawking temperature from scattering off the charged 2D black hole
The charged 2D black hole is visualized as presenting an potential barrier
to on-coming tachyon wave. Since this takes the complicated
form, an approximate form is used for scattering analysis. We
calculate the reflection and transmission coefficients for scattering of
tachyon off the charged 2D black hole. The Hawking temperature is also derived
from the reflection coefficient by Bogoliubov transformation. In the limit of
, we recover the Hawking temperature of the 2D dilaton black hole.Comment: 12 pages 3 figures, RevTeX, to obtain figures contact author
([email protected]
Instability of a two-dimensional extremal black hole
We consider the perturbation of tachyon about the extremal ground state of a
two-dimensional (2D) electrically charged black hole. It is found that the
presenting potential to on-coming tachyonic wave takes a double-humped barrier
well. This allows an exponentially growing mode with respect to time. This
extremal ground state is classically unstable. We conclude that the 2D extremal
electrically charged black hole cannot be a candidate for the stable endpoint
of the Hawking evaporation.Comment: 9 pages 2 figures, RevTeX, to be published in Phys. Rev D, to obtain
gifures contact Author ([email protected]
Propagating waves in an extremal black string
We investigate the black string in the context of the string theories. It is
shown that the graviton is the only propagating mode in the (2+1)--dimensional
extremal black string background. Both the dilation and axion turn out to be
non-propagating modes.Comment: Minor corrections, 11 pages in ReVTeX, no figure
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