5,763 research outputs found
Exact Asymptotics for the Random Coding Error Probability
Error probabilities of random codes for memoryless channels are considered in
this paper. In the area of communication systems, admissible error probability
is very small and it is sometimes more important to discuss the relative gap
between the achievable error probability and its bound than to discuss the
absolute gap. Scarlett et al. derived a good upper bound of a random coding
union bound based on the technique of saddlepoint approximation but it is not
proved that the relative gap of their bound converges to zero. This paper
derives a new bound on the achievable error probability in this viewpoint for a
class of memoryless channels. The derived bound is strictly smaller than that
by Scarlett et al. and its relative gap with the random coding error
probability (not a union bound) vanishes as the block length increases for a
fixed coding rate.Comment: Full version of the paper in ISIT2015 with some corrections and
refinement
Spin-boson coupling in continuous-time quantum Monte Carlo
A vector bosonic field coupled to the electronic spin is treated by means of
the continuous-time quantum Monte Carlo method. In the Bose Kondo model with a
sub-Ohmic density of states with s=0.2,
two contributions to the spin susceptibility, the Curie term T^{-1} and the
term T^{-s} due to bosonic fluctuations, are observed separately. This result
indicates the existence of a residual moment and a hidden critical behavior. By
including hybridization with itinerant electrons, a quantum critical point is
identified between this local-moment state and the Kondo singlet state. It is
demonstrated that the energy scale of the bosonic fluctuations is not affected
by the quantum phase transition.Comment: 8 pages, 7 figure
Two-Particle Self-Consistent Approach to Anisotropic Superconductivity
A nonperturbative approach to anisotropic superconductivity is developed
based on the idea of two-particle self-consistent (TPSC) theory by Vilk and
Tremblay. A sum-rule which the momentum-dependent pairing susceptibility
satisfies is derived. An effective pairing interaction between quasiparticles
is determined so that the susceptibility should fulfill this exact sum-rule, in
which fluctuations belonging to different symmetries couple at finite momentum.
It is demonstrated that the mode coupling between d-wave and s-wave pairing
fluctuations leads to suppression of the d-wave fluctuation near the Mott
insulator.Comment: 7 pages, 5 figure
Optimality of Thompson Sampling for Gaussian Bandits Depends on Priors
In stochastic bandit problems, a Bayesian policy called Thompson sampling
(TS) has recently attracted much attention for its excellent empirical
performance. However, the theoretical analysis of this policy is difficult and
its asymptotic optimality is only proved for one-parameter models. In this
paper we discuss the optimality of TS for the model of normal distributions
with unknown means and variances as one of the most fundamental example of
multiparameter models. First we prove that the expected regret of TS with the
uniform prior achieves the theoretical bound, which is the first result to show
that the asymptotic bound is achievable for the normal distribution model. Next
we prove that TS with Jeffreys prior and reference prior cannot achieve the
theoretical bound. Therefore the choice of priors is important for TS and
non-informative priors are sometimes risky in cases of multiparameter models
Surface defects and elliptic quantum groups
A brane construction of an integrable lattice model is proposed. The model is
composed of Belavin's R-matrix, Felder's dynamical R-matrix, the
Bazhanov-Sergeev-Derkachov-Spiridonov R-operator and some intertwining
operators. This construction implies that a family of surface defects act on
supersymmetric indices of four-dimensional supersymmetric
field theories as transfer matrices related to elliptic quantum groups.Comment: 31 pages. v2: minor changes and corrections; v3: minor improvements,
published versio
A simple merging algorithm for jet angular correlation studies
A tree level merging algorithm which guarantees the leading order (LO)
accuracy of angular correlations between jets is proposed and studied. The
algorithm is designed so that n-jet events are generated exclusively according
to the LO n-parton production cross section and each of the n-jet is close to
each of the n-parton in terms of the jet measure. As a result, the LO accuracy
of angular correlations between the n-jet is robust. Furthermore, as long as
the n-jet events are exclusively subjects to a study, only the LO n-parton
production cross section is needed and hence event generation is efficient.
Correlations in the azimuthal angle difference between the two highest
transverse momentum jets with large rapidity separations in the top quark pair
production are evaluated as examples. The algorithm is validated by discussing
numerical differences between its predictions and the predictions of a
well-established merging algorithm.Comment: 15 pages, 2 figure
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