Marc Höll

Marc Höll
Bar Ilan University | BIU · Department of Physics

PhD

About

17
Publications
1,272
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
179
Citations

Publications

Publications (17)
Article
The big jump principle explains the emergence of extreme events for physical quantities modelled by a sum of independent and identically distributed random variables which are heavy-tailed. Extreme events are large values of the sum and they are solely dominated by the largest summand called the big jump. Recently, the principle was introduced into...
Poster
Full-text available
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the distribution of the extreme value exhibits a non-analytical point in the middle of the support. We expose exact rel...
Poster
Full-text available
We present a general framework of detrending methods of fluctuation analysis of which detrended fluctuation analysis (DFA) is one prominent example. Another more recently introduced method is detrending moving average (DMA). Both methods are constructed differently but are similarly able to detect long-range correlations as well as anomalous diffus...
Preprint
Full-text available
The big jump principle explains the emergence of extreme events for physical quantities modelled by a sum of independent and identically distributed random variables which are heavy-tailed. Extreme events are large values of the sum and they are solely dominated by the largest summand called the big jump. Recently, the principle was introduced into...
Article
Full-text available
We study the ballistic Lévy walk stemming from an infinite mean traveling time between collision events. Our study focuses on the density of spreading particles all starting from a common origin, which is limited by a "light"cone -v0t<x<v0t. In particular we study this density close to its maximum in the vicinity of the light cone. The spreading de...
Article
Full-text available
We investigate extreme value theory for physical systems with a global conservation law which describes renewal processes, mass transport models, and long-range interacting spin models. As shown previously, a special feature is that the distribution of the extreme value exhibits a nonanalytical point in the middle of the support. We expose exact re...
Preprint
Full-text available
We study the ballistic L\'evy walk and obtain the far-tail of the distribution for the walker's position. When the position is of the order of the observation time, its distribution is described by the well-known Lamperti-arcsine law. However this law blows up at the far-tail which is nonphysical, in the sense that any finite time observation will...
Preprint
Full-text available
We investigate extreme value theory (EVT) of physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. A special feature is that the distribution of the extreme value exhibits a non-analytical point in the middle of the support. We reveal three exact relationships...
Article
Full-text available
Detrended fluctuation analysis (DFA) is one of the most widely used tools for the detection of long-range dependence in time series. Although DFA has found many interesting applications and has been shown to be one of the best performing detrending methods, its probabilistic foundations are still unclear. In this paper, we study probabilistic prope...
Article
Full-text available
We present a bottom-up derivation of fluctuation analysis with detrending for the detection of long-range correlations in the presence of additive trends or intrinsic nonstationarities. While the well-known detrended fluctuation analysis (DFA) and detrending moving average (DMA) were introduced ad hoc, we claim basic principles for such methods whe...
Preprint
We present a general framework of detrending methods of fluctuation analysis of which detrended fluctuation analysis (DFA) is one prominent example. Another more recently introduced method is detrending moving average (DMA). Both methods are constructed differently but are similarly able to detect long-range correlations as well as anomalous diffus...
Preprint
We present a general framework of detrending methods of fluctuation analysis of which detrended fluctuation analysis (DFA) is one prominent example. Another more recently introduced method is detrending moving average (DMA). Both methods are constructed differently but are similarly able to detect long-range correlations as well as anomalous diffus...
Preprint
Full-text available
The detrended fluctuation analysis (DFA) is one of the most widely used tools for the detection of long-range correlations in time series. Although DFA has found many interesting applications and has been shown as one of the best performing detrending methods, its probabilistic foundations are still unclear. In this paper we study probabilistic pro...
Article
We study global mean surface temperature records since 1850 and their potential forcings. We find long range correlations by the method of Detrended Fluctuation Analysis in most data sets, in agreement with previous studies. As a predictive model, we employ a zero‐dimensional energy balance model without memory that reproduces temperature data on t...
Article
Detrended fluctuation analysis (DFA) has been shown to be an effective method to study long-range correlation of nonstationary series. In principle, DFA considers FDFA2(s), the mean of variance around the local polynomial fit in segments with length s, and then estimates the scaling exponent αDFA in FDFA(s)∼sαDFA with varying s. Usually, the method...
Article
Full-text available
We derive an analytical expression for the fluctuation function of the detrended fluctuation analysis and state the relationship with the autocorrelation function for stationary processes. With this result we can investigate the scaling of the fluctuation function for short-range and long-range correlated processes. Furthermore we show that short-r...
Article
Full-text available
We derive an analytical expression for the fluctuation function of the first order autoregressive process AR(1) by means of the detrended fluctuation analysis (DFA). This process is short-range correlated and therefore the fluctuation exponent should be α = 1/2. However, the fluctuation function exhibits a crossover between a region with α > 1/2 an...

Network

Cited By

Projects

Projects (2)
Project
We developed the theoretical foundation of data tools (such as detrended fluctuation analysis) which estimate long-range correlations in non-stationary time series.
Project
Physical systems usually exhibit correlations. These must be incoorporated into the extreme value theory. The main goal is to develop tools for damage reduction of extreme events.