155 research outputs found
Bad configurations for random walk in random scenery and related subshifts
In this paper we consider an arbitrary irreducible random walk on , d1, with i.i.d. increments, together with an arbitrary i.i.d. random scenery. Walk and scenery are assumed to be independent. Random walk in random scenery (RWRS) is the random process where time is indexed by , and at each unit of time both the step taken by the walk and the scenery value at the site that is visited are registered. Bad configurations for RWRS are the discontinuity points of the conditional probability distribution for the configuration at the origin of time given the configuration at all other times. We show that the set of bad configurations is non-empty. We give a complete description of this set and compute its probability under the random scenery measure. Depending on the type of random walk, this probability may be zero or positive. For simple symmetric random walk we get three different types of behavior depending on whether d=1,2, d=3,4 or d5. Our classification is actually valid for a class of subshifts having a certain determinative property, which we call specifiable, of which RWRS is an example. We also consider bad configurations w.r.t. a finite time interval (replacing the origin) and obtain an almost complete generalization of our results. Remarkably, this extension turns out to be somewhat delicate
Bad configurations for random walk in random scenery and related subshifts
Article / Letter to editorMathematisch Instituu
Bad configurations for random walk in random scenery and related subshifts
Analysis and Stochastic
Curvature singularity of the distributional BTZ black hole geometry
For the non-rotating BTZ black hole, the distributional curvature tensor
field is found. It is shown to have singular parts proportional to a
-distribution with support at the origin. This singularity is related,
through Einstein field equations, to a point source. Coordinate invariance and
independence on the choice of differentiable structure of the results are
addressed.Comment: Latex, 7 page
An Equivalence Between Momentum and Charge in String Theory
It is shown that for a translationally invariant solution to string theory,
spacetime duality interchanges the momentum in the symmetry direction and the
axion charge per unit length. As one application, we show explicitly that
charged black strings are equivalent to boosted (uncharged) black strings. The
extremal black strings (which correspond to the field outside of a fundamental
macroscopic string) are equivalent to plane fronted waves describing strings
moving at the speed of light.Comment: 10 page
Gott Time Machines, BTZ Black Hole Formation, and Choptuik Scaling
We study the formation of BTZ black holes by the collision of point
particles. It is shown that the Gott time machine, originally constructed for
the case of vanishing cosmological constant, provides a precise mechanism for
black hole formation. As a result, one obtains an exact analytic understanding
of the Choptuik scaling.Comment: 6 pages, Late
Gravitational collapse in 2+1 dimensional AdS spacetime
We present results of numerical simulations of the formation of black holes
from the gravitational collapse of a massless, minimally-coupled scalar field
in 2+1 dimensional, axially-symmetric, anti de-Sitter (AdS) spacetime. The
geometry exterior to the event horizon approaches the BTZ solution, showing no
evidence of scalar `hair'. To study the interior structure we implement a
variant of black-hole excision, which we call singularity excision. We find
that interior to the event horizon a strong, spacelike curvature singularity
develops. We study the critical behavior at the threshold of black hole
formation, and find a continuously self-similar solution and corresponding
mass-scaling exponent of approximately 1.2. The critical solution is universal
to within a phase that is related to the angle deficit of the spacetime.Comment: 31 pages, 20 figures, LaTeX. Replaced with version to be published in
Phys. Rev.
Form factors at strong coupling via a Y-system
We compute form factors in planar N=4 Super Yang-Mills at strong coupling.
Namely we consider the overlap between an operator insertion and 2n gluons.
Through the gauge/string duality these are given by minimal surfaces in AdS
space. The surfaces end on an infinite periodic sequence of null segments at
the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We
derive set of functional equations for the cross ratios as functions of the
spectral parameter. These equations are of the form of a Y-system. The integral
form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by
the free energy of the TBA system or critical value of Yang-Yang functional. We
consider a restricted set of operators which have small conformal dimension
Interior Structure of a Charged Spinning Black Hole in -Dimensions
The phenomenon of mass inflation is shown to occur for a rotating black hole.
We demonstrate this feature in dimensions by extending the charged
spinning BTZ black hole to Vaidya form. We find that the mass function diverges
in a manner quantitatively similar to its static counterparts in ,
and dimensions.Comment: 5 pages, 2 figures (appended as postscript files), WATPHYS-TH94/0
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