14,038 research outputs found
A simple asymmetric evolving random network
We introduce a new oriented evolving graph model inspired by biological
networks. A node is added at each time step and is connected to the rest of the
graph by random oriented edges emerging from older nodes. This leads to a
statistical asymmetry between incoming and outgoing edges. We show that the
model exhibits a percolation transition and discuss its universality. Below the
threshold, the distribution of component sizes decreases algebraically with a
continuously varying exponent depending on the average connectivity. We prove
that the transition is of infinite order by deriving the exact asymptotic
formula for the size of the giant component close to the threshold. We also
present a thorough analysis of aging properties. We compute local-in-time
profiles for the components of finite size and for the giant component, showing
in particular that the giant component is always dense among the oldest nodes
but invades only an exponentially small fraction of the young nodes close to
the threshold.Comment: 33 pages, 3 figures, to appear in J. Stat. Phy
Loewner Chains
These lecture notes on 2D growth processes are divided in two parts. The
first part is a non-technical introduction to stochastic Loewner evolutions
(SLEs). Their relationship with 2D critical interfaces is illustrated using
numerical simulations. Schramm's argument mapping conformally invariant
interfaces to SLEs is explained. The second part is a more detailed
introduction to the mathematically challenging problems of 2D growth processes
such as Laplacian growth, diffusion limited aggregation (DLA), etc. Their
description in terms of dynamical conformal maps, with discrete or continuous
time evolution, is recalled. We end with a conjecture based on possible
dendritic anomalies which, if true, would imply that the Hele-Shaw problem and
DLA are in different universality classes.Comment: 46 pages, 21 figure
On Root Multiplicities of Some Hyperbolic Kac-Moody Algebras
Using the coset construction, we compute the root multiplicities at level
three for some hyperbolic Kac-Moody algebras including the basic hyperbolic
extension of and .Comment: 10 pages, LaTe
Sailing the Deep Blue Sea of Decaying Burgers Turbulence
We study Lagrangian trajectories and scalar transport statistics in decaying
Burgers turbulence. We choose velocity fields, solutions of the inviscid
Burgers equation, whose probability distributions are specified by Kida's
statistics. They are time-correlated, not time-reversal invariant and not
Gaussian. We discuss in some details the effect of shocks on trajectories and
transport equations. We derive the inviscid limit of these equations using a
formalism of operators localized on shocks. We compute the probability
distribution functions of the trajectories although they do not define Markov
processes. As physically expected, these trajectories are statistically
well-defined but collapse with probability one at infinite time. We point out
that the advected scalars enjoy inverse energy cascades. We also make a few
comments on the connection between our computations and persistence problems.Comment: 18 pages, one figure in eps format, Latex, published versio
The performance of amateur traders on a public internet site: a case of a stock-exchange contest
We analyze a very thorough data base, including all of the bid/ask orders and daily portfolio values of more than 600 on-line amateur traders from February 2007 to June 2009. These traders were taking part in a stock-exchange contest proposed by the French Internet stock-exchange site Zonebourse. More than 80% of traders lose relative to the market. Their relative average annual performance varies from -38% to -60%, depending on the method used. In absolute, more than 99% of traders lose and face drastic losses: on average, portfolio values fall from an initial value of 100 to a terminal value of 7 in the 29 months covered here. When we include the rewards offered by the contest, average performance becomes -13% a year. However, only two deciles continue to beat the market. From an initial value of 100 the final value is 28 including rewards, but 95% of traders still lose in absolute. There is no clear performance persistence for traders. Are the best traders just lucky then? Focusing on contest winners, the long-term transition analysis suggests a long-term probability of staying in the best decile which is greater than chance. We thus cannot reject a âstar effectâ of staying in the best decile. However, the great majority of amateurs do seem to be e-pigeons. Online trading may just be costly entertainment, like casino gambling.Behavioral finance, finance, online trading, amateur traders , e-pigeons, trade losses
Spikes in quantum trajectories
A quantum system subjected to a strong continuous monitoring undergoes
quantum jumps. This very well known fact hides a neglected subtlety: sharp
scale-invariant fluctuations invariably decorate the jump process even in the
limit where the measurement rate is very large. This article is devoted to the
quantitative study of these remaining fluctuations, which we call spikes, and
to a discussion of their physical status. We start by introducing a classical
model where the origin of these fluctuations is more intuitive and then jump to
the quantum realm where their existence is less intuitive. We compute the exact
distribution of the spikes for a continuously monitored qubit. We conclude by
discussing their physical and operational relevance.Comment: 8 pages, 8 figure
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