899,090 research outputs found
Constructing Sublinear Expectations on Path Space
We provide a general construction of time-consistent sublinear expectations
on the space of continuous paths. It yields the existence of the conditional
G-expectation of a Borel-measurable (rather than quasi-continuous) random
variable, a generalization of the random G-expectation, and an optional
sampling theorem that holds without exceptional set. Our results also shed
light on the inherent limitations to constructing sublinear expectations
through aggregation.Comment: 28 pages; forthcoming in 'Stochastic Processes and their
Applications
Derived rules for predicative set theory: an application of sheaves
We show how one may establish proof-theoretic results for constructive
Zermelo-Fraenkel set theory, such as the compactness rule for Cantor space and
the Bar Induction rule for Baire space, by constructing sheaf models and using
their preservation properties
Compactness and finite forcibility of graphons
Graphons are analytic objects associated with convergent sequences of graphs.
Problems from extremal combinatorics and theoretical computer science led to a
study of graphons determined by finitely many subgraph densities, which are
referred to as finitely forcible. Following the intuition that such graphons
should have finitary structure, Lovasz and Szegedy conjectured that the
topological space of typical vertices of a finitely forcible graphon is always
compact. We disprove the conjecture by constructing a finitely forcible graphon
such that the associated space is not compact. The construction method gives a
general framework for constructing finitely forcible graphons with non-trivial
properties
Constructing a Space from the System of Geodesic Equations
Given a space it is easy to obtain the system of geodesic equations on it. In
this paper the inverse problem of reconstructing the space from the geodesic
equations is addressed. A procedure is developed for obtaining the metric
tensor from the Christoffel symbols. The procedure is extended for determining
if a second order quadratically semi-linear system can be expressed as a system
of geodesic equations, provided it has terms only quadratic in the first
derivative apart from the second derivative term. A computer code has been
developed for dealing with larger systems of geodesic equations
Quantum Geometry as a Relational Construct
The problem of constructing a quantum theory of gravity is considered from a
novel viewpoint. It is argued that any consistent theory of gravity should
incorporate a relational character between the matter constituents of the
theory.
In particular, the traditional approach of quantizing a space-time metric is
criticized and two possible avenues for constructing a satisfactory theory are
put forward.Comment: 14 pages, revtex file. Submitted to MPL
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