Doubts on the existence of an exponential bound were raised by
Catterall et al [74], who considered the behaviour of
in
. Their data (taken for
) were consistent with a leading factorial behaviour
. The same scenario was favoured by de Bakker and Smit [89
], who performed further investigations of
. Subsequently, Ambjørn and Jurkiewicz [12] and Brügmann and Marinari [60] added further data points at
and
respectively. Their numerical results, as well as those by
Catterall et al [78], who employed an alternative method for measuring
, favour the existence of an exponential bound, although they
cannot claim to be conclusive.
There have also been theoretical arguments for the existence
of an exponential bound, based on the proofs of such bounds for
the counting of minimal geodesic ball coverings of Riemannian
spaces of bounded geometry [68,
26], and the counting of discrete curvature assignments to
unordered sets of bones [8].
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Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll http://www.livingreviews.org/lrr-1998-13 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |