Pinning on a defect line: characterization of marginal disorder relevance and sharp asymptotics for the critical point shift

The effect of disorder for pinning models is a subject which has attracted much attention in theoretical physics and rigorous mathematical physics. A peculiar point of interest is the question of coincidence of the quenched and annealed critical point for a small amount of disorder. The question has been mathematically settled in most cases in the last few years, giving in particular a rigorous validation of the Harris Criterion on disorder relevance. However, the marginal case, where the return probability exponent is equal to $1/2$, i.e. where the inter-arrival law of the renewal process is given by $K(n)=n^{-3/2}\phi(n)$ where $\phi$ is a slowly varying function, has been left partially open. In this paper, we give a complete answer to the question by proving a simple necessary and sufficient criterion on the return probability for disorder relevance, which confirms earlier predictions from the literature. Moreover, we also provide sharp asymptotics on the critical point shift: in the case of the pinning (or wetting) of a one dimensional simple random walk, the shift of the critical point satisfies the following high temperature asymptotics $$\lim_{\beta\rightarrow 0}\beta^2\log h_c(\beta)= - \frac{\pi}{2}.$$ This gives a rigorous proof to a claim of B. Derrida, V. Hakim and J. Vannimenus (Journal of Statistical Physics, 1992).Comment: 34 Page

Classical and quantum anomalous diffusion in a system of 2δ\delta-kicked Quantum Rotors

We study the dynamics of cold atoms subjected to {\em pairs} of closely time-spaced $\delta$-kicks from standing waves of light. The classical phase space of this system is partitioned into momentum cells separated by trapping regions. In a certain range of parameters it is shown that the classical motion is well described by a process of anomalous diffusion. We investigate in detail the impact of the underlying classical anomalous diffusion on the quantum dynamics with special emphasis on the phenomenon of dynamical localization. Based on the study of the quantum density of probability, its second moment and the return probability we identify a region of weak dynamical localization where the quantum diffusion is still anomalous but the diffusion rate is slower than in the classical case. Moreover we examine how other relevant time scales such as the quantum-classical breaking time or the one related to the beginning of full dynamical localization are modified by the classical anomalous diffusion. Finally we discuss the relevance of our results for the understanding of the role of classical cantori in quantum mechanics.Comment: 9 pages, 3 figure

Women's Fertility and Employment Decisions under Two Political Systems - Comparing East and West Germany before Reunification

Over the last decades fertility rates have decreased in most developed countries, while female labour force participation has increased strongly over the same time period. To shed light on the relationship between women's fertility and employment decisions, we analyse their transitions to the first, second, and third child as well as their employment discontinuities following childbirth. Using new longitudinal datasets that cover the work and family life of women in the Federal Republic of Germany (FRG) and the German Democratic Republic (GDR) allows for taking into account two political regimes and drawing conclusions about the relevance of institutional factors for fertility and employment decisions. Our results suggest that in both parts of Germany women's probability of having a first child is negatively correlated with both employment and educational achievement. Regarding second and third birth risks, this negative correlation weakens. Analysing women's time spent out of the labour market following childbirth we find that in the East almost all mothers return to work within 18 months after birth. In the West, however, this proportion is much smaller and at the age when the child starts nursery school or school, women re-enter the labour market at higher rates. These results point to a strong influence of institutional circumstances, specifically the extent of public daycare provision. A multivariate analysis reveals a strong correlation between a woman's employment status prior to birth and her probability of re-entering the labour market afterwards.Female labour force participation, fertility

Extreme Market Risk - An Extreme Value Theory Approach

The phenomenon of the occurrence of rare yet extreme events, “Black Swans” in Taleb’s terminology, seems to be more apparent in financial markets around the globe. This means there is not only a need to design proper risk modelling techniques which can predict the probability of risky events in normal market conditions but also a requirement for tools which can assess the probabilities of rare financial events; like the recent Global Financial Crisis (2007-2008). An obvious candidate, when dealing with extreme financial events and the quantification of extreme market risk is Extreme Value Theory (EVT). This proves to be a natural statistical modelling technique of relevance. Extreme Value Theory provides well established statistical models for the computation of extreme risk measures like the Return Level, Value at Risk and Expected Shortfall. In this paper we apply Univariate Extreme Value Theory to model extreme market risk for the ASX-All Ordinaries (Australian) index and the S&P-500 (USA) Index. We demonstrate that EVT can be successfully applied to financial market return series for predicting static VaR, CVaR or Expected Shortfall (ES) and expected Return Level and also daily VaR using a GARCH(1,1) and EVT based dynamic approach

How historical information can improve estimation and prediction of extreme coastal water levels: application to the Xynthia event at La Rochelle (France)

International audienceThe knowledge of extreme coastal water levels is useful for coastal flooding studies or the design of coastal defences. While deriving such extremes with standard analyses using tide-gauge measurements, one often needs to deal with limited effective duration of observation which can result in large statistical uncertainties. This is even truer when one faces the issue of outliers, those particularly extreme values distant from the others which increase the uncertainty on the results. In this study, we investigate how historical information , even partial, of past events reported in archives can reduce statistical uncertainties and relativise such outlying observations. A Bayesian Markov chain Monte Carlo method is developed to tackle this issue. We apply this method to the site of La Rochelle (France), where the storm Xynthia in 2010 generated a water level considered so far as an outlier. Based on 30 years of tide-gauge measurements and 8 historical events, the analysis shows that (1) integrating historical information in the analysis greatly reduces statistical uncertainties on return levels (2) Xynthia's water level no longer appears as an outlier, (3) we could have reasonably predicted the annual exceedance probability of that level beforehand (predictive probability for 2010 based on data until the end of 2009 of the same order of magnitude as the standard es-timative probability using data until the end of 2010). Such results illustrate the usefulness of historical information in extreme value analyses of coastal water levels, as well as the relevance of the proposed method to integrate heterogeneous data in such analyses

Context-Gated Statistical Learning and Its Role in Visual-Saccadic Decisions

Adaptive behavior in a nonstationary world requires humans to learn and track the statistics of the environment. We examined the mechanisms of adaptation in a nonstationary environment in the context of visual-saccadic inhibition of return (IOR). IOR is adapted to the likelihood that return locations will be refixated in the near future. We examined 2 potential learning mechanisms underlying adaptation: (a) a local tracking or priming mechanism that facilitates behavior that is consistent with recent experience and (b) a mechanism that supports retrieval of knowledge of the environmental statistics based on the contextual features of the environment. Participants generated sequences of 2 saccadic eye movements in conditions where the probability that the 2nd saccade was directed back to the previously fixated location varied from low (.17) to high (.50). In some conditions, the contingency was signaled by a contextual cue (the shape of the movement cue). Adaptation occurred in the absence of contextual signals but was more pronounced in the presence of contextual cues. Adaptation even occurred when different contingencies were randomly intermixed, showing the parallel formation of multiple associations between context and statistics. These findings are accounted for by an evidence accumulation framework in which the resting baseline of decision alternatives is adjusted on a trial-by-trial basis. This baseline tracks the subjective prior beliefs about the behavioral relevance of the different alternatives and is updated on the basis of the history of recent events and the contextual features of the current environment