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Quantum stochastic calculus on interacting Fock spaces: semimartingale estimates and stochastic integral
Full text linkVacuum distribution, norm and spectral properties for sums of monotone position operators
No full textWe investigate the spectrum for partial sums of m
position (or gaussian) operators on monotone Fock space based
on . In the basic case of the rst consecutive operators, we
prove it coincides with the support of the vacuum distribution.
Thus, the right endpoint of the support gives their norm. In the
general case, we get the last property for norm still holds. As
the single position operator has the vacuum symmetric Bernoulli
law, and the whole of them is a monotone independent family of
random variables, the vacuum distribution for partial sums of n
operators can be seen as the monotone binomial with n trials. It
is a discrete measure supported on a nite set, and we exhibit
recurrence formulas to compute its atoms and probability function
as well. Moreover, lower and upper bounds for the right endpoints
of the supports are given
Failure of the Ryll-Nardzewski theorem on the CAR algebra
Full text linkSpreadability of a sequence of random variables is a distri-butional symmetry that is implemented by suitable actions of J_Z, the unital semigroup of strictly increasing maps on Z with cofinite range. We show that J_Zis left amenable but not right amenable, although it does admit a right Følner sequence. This enables us to prove that on the CAR algebra CAR(Z) there exist spreadable states that fail to be exchangeable. Moreover, we also show that on CAR(Z) there exist stationary states that fail to be spreadable
Tail algebras for monotone and q-deformed exchangeable stochastic processes
Full text linkWe compute the tail algebras of exchangeable monotone stochastic processes. This allows
us to prove the analogue of de Finetti’s theorem for this type of processes. In addition,
since the vacuum state on the q-deformed C∗-algebra is the only exchangeable state when
q < 1 , we draw our attention to its tail algebra, which turns out to obey a zero-one law
A projective central limit theorem and an interacting Fock space representation for the limit process
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
WEAKLY MONOTONE FOCK SPACE AND MONOTONE CONVOLUTION OF THE WIGNER LAW
Full text linkWe study the distribution (w.r.t. the vacuum state)
of family of partial sums Sm of position operators on weakly monotone
Fock space. We show that any single operator has the Wigner
law, and an arbitrary family of them (with the index set linearly
ordered) is a collection of monotone independent random variables.
It turns out that our problem equivalently consists in nding the
m-fold monotone convolution of the semicircle law. For m = 2
we compute the explicit distribution. For any m > 2 we give the
moments of the measure, and show it is absolutely continuous and
compactly supported on a symmetric interval whose endpoints can
be found by a recurrence relation
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