19,507 research outputs found
The Hole Probability for Gaussian Entire Functions
We study the hole probability of Gaussian random entire functions. More
specifically, we work with entire functions in Taylor series form with i.i.d
complex Gaussian coefficients. A hole is the event where the function has no
zeros in a disc of radius r. We find exact asymptotics for the rate of decay of
the hole probability for large values of r, outside a small exceptional set
(which is deterministic).Comment: 1 figur
orbifold compactification -- the origin of realistic free fermionic models
All the realistic free fermionic models utilize a set of basis vectors, the
NAHE set, that correspond to orbifold compactification with
nontrivial background fields. I argue that the realistic features of free
fermionic models, like the number of generations and the fermion mass spectrum
are due to the underlying orbifold compactification.Comment: 4 pages, latex, To appear in proceedings of the Beyond the Standard
Model IV Conference, Lake Tahoe, CA, Dec 13-18, 1994. IASSNS preprint number
is corrected
The Function of the Second Postulate in Special Relativity
Many authors noted that the principle of relativity, together with space-time
symmetries, suffices to derive Lorentz-like coordinate transformations between
inertial frames. These contain a free parameter, , (equal to in
special relativity) which is usually claimed to be empirically determinable, so
that special relativity does not need the postulate of constancy of the speed
of light. I analyze this claim and find that all methods destined to measure
fail without further assumptions, similar to the second postulate.
Specifically, measuring requires a signal that travels identically in
opposite directions (this is unrelated to the conventionality of
synchronization, as the one-postulate program implicitly selects the standard
synchronization convention). Positing such a property about light is logically
weaker than Einstein's second postulate but suffices to recover special
relativity in full
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