175,000 research outputs found
Exact convergence rates in central limit theorems for a branching random walk with a random environment in time
Chen [Ann. Appl. Probab. {\bf 11} (2001), 1242--1262] derived exact
convergence rates in a central limit theorem and a local limit theorem for a
supercritical branching Wiener process.We extend Chen's results to a branching
random walk under weaker moment conditions. For the branching Wiener process,
our results sharpen Chen's by relaxing the second moment condition used by Chen
to a moment condition of the form \E X (\ln^+X )^{1+\lambda}< \infty. In the
rate functions that we find for a branching random walk, we figure out some new
terms which didn't appear in Chen's work.The results are established in the
more general framework, i.e. for a branching random walk with a random
environment in time.The lack of the second moment condition for the offspring
distribution and the fact that the exponential moment does not exist
necessarily for the displacements make the proof delicate; the difficulty is
overcome by a careful analysis of martingale convergence using a truncating
argument. The analysis is significantly more awkward due to the appearance of
the random environment.Comment: Corrected version of https://hal.archives-ouvertes.fr/hal-01095105.
arXiv admin note: text overlap with arXiv:1504.01181 by other author
Regenesis and quantum traversable wormholes
Recent gravity discussions of a traversable wormhole indicate that in
holographic systems signals generated by a source could reappear long after
they have dissipated, with the need of only performing some simple operations.
In this paper we argue the phenomenon, to which we refer as "regenesis", is
universal in general quantum chaotic many-body systems, and elucidate its
underlying physics. The essential elements behind the phenomenon are: (i)
scrambling which in a chaotic system makes out-of-time-ordered correlation
functions (OTOCs) vanish at large times; (ii) the entanglement structure of the
state of the system. The latter aspect also implies that the regenesis
phenomenon requires fine tuning of the initial state. Compared to other
manifestations of quantum chaos such as the initial growth of OTOCs which deals
with early times, and a random matrix-type energy spectrum which reflects very
large time behavior, regenesis concerns with intermediate times, of order the
scrambling time of a system. We also study the phenomenon in detail in general
two-dimensional conformal field theories in the large central charge limit, and
highlight some interesting features including a resonant enhancement of
regenesis signals near the scrambling time and their oscillations in coupling.
Finally, we discuss gravity implications of the phenomenon for systems with a
gravity dual, arguing that there exist regimes for which traversability of a
wormhole is quantum in nature, i.e. cannot be associated with a semi-classical
spacetime causal structure
Variational formulation of hybrid problems for fully 3-D transonic flow with shocks in rotor
Based on previous research, the unified variable domain variational theory of hybrid problems for rotor flow is extended to fully 3-D transonic rotor flow with shocks, unifying and generalizing the direct and inverse problems. Three variational principles (VP) families were established. All unknown boundaries and flow discontinuities (such as shocks, free trailing vortex sheets) are successfully handled via functional variations with variable domain, converting almost all boundary and interface conditions, including the Rankine Hugoniot shock relations, into natural ones. This theory provides a series of novel ways for blade design or modification and a rigorous theoretical basis for finite element applications and also constitutes an important part of the optimal design theory of rotor bladings. Numerical solutions to subsonic flow by finite elements with self-adapting nodes given in Refs., show good agreement with experimental results
Research on inverse, hybrid and optimization problems in engineering sciences with emphasis on turbomachine aerodynamics: Review of Chinese advances
Advances in inverse design and optimization theory in engineering fields in China are presented. Two original approaches, the image-space approach and the variational approach, are discussed in terms of turbomachine aerodynamic inverse design. Other areas of research in turbomachine aerodynamic inverse design include the improved mean-streamline (stream surface) method and optimization theory based on optimal control. Among the additional engineering fields discussed are the following: the inverse problem of heat conduction, free-surface flow, variational cogeneration of optimal grid and flow field, and optimal meshing theory of gears
Second and third orders asymptotic expansions for the distribution of particles in a branching random walk with a random environment in time
Consider a branching random walk in which the offspring distribution and the
moving law both depend on an independent and identically distributed random
environment indexed by the time.For the normalised counting measure of the
number of particles of generation in a given region, we give the second and
third orders asymptotic expansions of the central limit theorem under rather
weak assumptions on the moments of the underlying branching and moving laws.
The obtained results and the developed approaches shed light on higher order
expansions. In the proofs, the Edgeworth expansion of central limit theorems
for sums of independent random variables, truncating arguments and martingale
approximation play key roles. In particular, we introduce a new martingale,
show its rate of convergence, as well as the rates of convergence of some known
martingales, which are of independent interest.Comment: Accepted by Bernoull
- …