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 $A_1^{(1)}$ and $E_{10}$.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 “star effect” 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