1,260,837 research outputs found
Density of near-extreme events
We provide a quantitative analysis of the phenomenon of crowding of
near-extreme events by computing exactly the density of states (DOS) near the
maximum of a set of independent and identically distributed random variables.
We show that the mean DOS converges to three different limiting forms depending
on whether the tail of the distribution of the random variables decays slower
than, faster than, or as a pure exponential function. We argue that some of
these results would remain valid even for certain {\em correlated} cases and
verify it for power-law correlated stationary Gaussian sequences. Satisfactory
agreement is found between the near-maximum crowding in the summer temperature
reconstruction data of western Siberia and the theoretical prediction.Comment: 4 pages, 3 figures, revtex4. Minor corrections, references updated.
This is slightly extended version of the Published one (Phys. Rev. Lett.
Extreme Events in Nonlinear Lattices
The spatiotemporal complexity induced by perturbed initial excitations
through the development of modulational instability in nonlinear lattices with
or without disorder, may lead to the formation of very high amplitude,
localized transient structures that can be named as extreme events. We analyze
the statistics of the appearance of these collective events in two different
universal lattice models; a one-dimensional nonlinear model that interpolates
between the integrable Ablowitz-Ladik (AL) equation and the nonintegrable
discrete nonlinear Schr\"odinger (DNLS) equation, and a two-dimensional
disordered DNLS equation. In both cases, extreme events arise in the form of
discrete rogue waves as a result of nonlinear interaction and rapid coalescence
between mobile discrete breathers. In the former model, we find power-law
dependence of the wave amplitude distribution and significant probability for
the appearance of extreme events close to the integrable limit. In the latter
model, more importantly, we find a transition in the the return time
probability of extreme events from exponential to power-law regime. Weak
nonlinearity and moderate levels of disorder, corresponding to weak chaos
regime, favour the appearance of extreme events in that case.Comment: Invited Chapter in a Special Volume, World Scientific. 19 pages, 9
figure
Outliers, Extreme Events and Multiscaling
Extreme events have an important role which is sometime catastrophic in a
variety of natural phenomena including climate, earthquakes and turbulence, as
well as in man-made environments like financial markets. Statistical analysis
and predictions in such systems are complicated by the fact that on the one
hand extreme events may appear as "outliers" whose statistical properties do
not seem to conform with the bulk of the data, and on the other hands they
dominate the (fat) tails of probability distributions and the scaling of high
moments, leading to "abnormal" or "multi"-scaling. We employ a shell model of
turbulence to show that it is very useful to examine in detail the dynamics of
onset and demise of extreme events. Doing so may reveal dynamical scaling
properties of the extreme events that are characteristic to them, and not
shared by the bulk of the fluctuations. As the extreme events dominate the
tails of the distribution functions, knowledge of their dynamical scaling
properties can be turned into a prediction of the functional form of the tails.
We show that from the analysis of relatively short time horizons (in which the
extreme events appear as outliers) we can predict the tails of the probability
distribution functions, in agreement with data collected in very much longer
time horizons. The conclusion is that events that may appear unpredictable on
relatively short time horizons are actually a consistent part of a multiscaling
statistics on longer time horizons.Comment: 11 pages, 14 figures included, PRE submitte
Impact and Recovery Process of Mini Flash Crashes: An Empirical Study
In an Ultrafast Extreme Event (or Mini Flash Crash), the price of a traded
stock increases or decreases strongly within milliseconds. We present a
detailed study of Ultrafast Extreme Events in stock market data. In contrast to
popular belief, our analysis suggests that most of the Ultrafast Extreme Events
are not primarily due to High Frequency Trading. In at least 60 percent of the
observed Ultrafast Extreme Events, the main cause for the events are large
market orders. In times of financial crisis, large market orders are more
likely which can be linked to the significant increase of Ultrafast Extreme
Events occurrences. Furthermore, we analyze the 100 trades following each
Ultrafast Extreme Events. While we observe a tendency of the prices to
partially recover, less than 40 percent recover completely. On the other hand
we find 25 percent of the Ultrafast Extreme Events to be almost recovered after
only one trade which differs from the usually found price impact of market
orders
- …