2,449 research outputs found
Quantum Dilaton Gravity in Two Dimensions with Fermionic Matter
Path integral quantization of generic two-dimensional dilaton gravity
non-minimally coupled to a Dirac fermion is performed. After integrating out
geometry exactly, perturbation theory is employed in the matter sector to
derive the lowest order gravitational vertices. Consistency with the case of
scalar matter is found and issues of relevance for bosonisation are pointed
out.Comment: 27 pages, 3 figures, v2: final version, added references, sec. 2
partially rewritten, some amendments, to be published in Class. Quant. Gra
A probabilistic weak formulation of mean field games and applications
Mean field games are studied by means of the weak formulation of stochastic
optimal control. This approach allows the mean field interactions to enter
through both state and control processes and take a form which is general
enough to include rank and nearest-neighbor effects. Moreover, the data may
depend discontinuously on the state variable, and more generally its entire
history. Existence and uniqueness results are proven, along with a procedure
for identifying and constructing distributed strategies which provide
approximate Nash equlibria for finite-player games. Our results are applied to
a new class of multi-agent price impact models and a class of flocking models
for which we prove existence of equilibria
Ramifications of Lineland
A non-technical overview on gravity in two dimensions is provided.
Applications discussed in this work comprise 2D type 0A/0B string theory, Black
Hole evaporation/thermodynamics, toy models for quantum gravity, for numerical
General Relativity in the context of critical collapse and for solid state
analogues of Black Holes. Mathematical relations to integrable models,
non-linear gauge theories, Poisson-sigma models, KdV surfaces and
non-commutative geometry are presented.Comment: 45 pages, 3 eps figures, proceedings contribution to 5th Workshop on
Quantization, Dualities & Integrable Systems in Denizli, Turkey; v2: added
refs. and a comment on phase transitions: v3: minor cosmetic chang
Mean field games with common noise
A theory of existence and uniqueness is developed for general stochastic
differential mean field games with common noise. The concepts of strong and
weak solutions are introduced in analogy with the theory of stochastic
differential equations, and existence of weak solutions for mean field games is
shown to hold under very general assumptions. Examples and counter-examples are
provided to enlighten the underpinnings of the existence theory. Finally, an
analog of the famous result of Yamada and Watanabe is derived, and it is used
to prove existence and uniqueness of a strong solution under additional
assumptions
Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit
Subspace clustering methods based on , or nuclear norm
regularization have become very popular due to their simplicity, theoretical
guarantees and empirical success. However, the choice of the regularizer can
greatly impact both theory and practice. For instance, regularization
is guaranteed to give a subspace-preserving affinity (i.e., there are no
connections between points from different subspaces) under broad conditions
(e.g., arbitrary subspaces and corrupted data). However, it requires solving a
large scale convex optimization problem. On the other hand, and
nuclear norm regularization provide efficient closed form solutions, but
require very strong assumptions to guarantee a subspace-preserving affinity,
e.g., independent subspaces and uncorrupted data. In this paper we study a
subspace clustering method based on orthogonal matching pursuit. We show that
the method is both computationally efficient and guaranteed to give a
subspace-preserving affinity under broad conditions. Experiments on synthetic
data verify our theoretical analysis, and applications in handwritten digit and
face clustering show that our approach achieves the best trade off between
accuracy and efficiency.Comment: 13 pages, 1 figure, 2 tables. Accepted to CVPR 2016 as an oral
presentatio
Transversal interface dynamics of a front connecting a stripe pattern to a uniform state
Interfaces in two-dimensional systems exhibit unexpected complex dynamical
behaviors, the dynamics of a border connecting a stripe pattern and a uniform
state is studied. Numerical simulations of a prototype isotropic model, the
subcritical Swift-Hohenberg equation, show that this interface has transversal
spatial periodic structures, zigzag dynamics and complex coarsening process.
Close to a spatial bifurcation, an amended amplitude equation and a
one-dimensional interface model allow us to characterize the dynamics exhibited
by this interface.Comment: 4 pages. To be published in Europhysics Letter
Black Hole Thermodynamics and Hamilton-Jacobi Counterterm
We review the construction of the universal Hamilton-Jacobi counterterm for
dilaton gravity in two dimensions, derive the corresponding result in the
Cartan formulation and elaborate further upon black hole thermodynamics and
semi-classical corrections. Applications include spherically symmetric black
holes in arbitrary dimensions with Minkowski- or AdS-asymptotics, the BTZ black
hole and black holes in two-dimensional string theory.Comment: 9 pages, proceedings contribution to QFEXT07 submitted to IJMPA, v2:
added Re
One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model
This paper carries forward a series of articles describing our enterprise to
construct a gauge equivalent for the -deformed non-commutative
model originally introduced by Gurau et al. arXiv:0802.0791. It is shown that
breaking terms of the form used by Vilar et al. arXiv:0902.2956 and ourselves
arXiv:0901.1681 to localize the BRST covariant operator
lead to difficulties concerning renormalization. The reason is that this
dimensionless operator is invariant with respect to any symmetry of the model,
and can be inserted to arbitrary power. In the present article we discuss
explicit one-loop calculations, and analyze the mechanism the mentioned
problems originate from.Comment: v2: minor corrections and references added; v3: published versio
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