Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

2.5K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
2.5K
Probability in Statistics01:14

Probability in Statistics

12.6K
Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
12.6K
Probability Histograms01:17

Probability Histograms

11.2K
A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
11.2K
Random Variables01:09

Random Variables

11.6K
A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
11.6K
Poisson Probability Distribution01:09

Poisson Probability Distribution

7.8K
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
7.8K
Probability Distributions01:32

Probability Distributions

6.9K
 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
6.9K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Probing and modeling cell-cell communication in 2D biomimetic tissues.

Soft matter·2026
Same author

Flips reveal the universal impact of memory on random explorations.

Nature communications·2025
Same author

Exact Propagators of One-Dimensional Self-Interacting Random Walks.

Physical review letters·2024
Same author

Long-term memory induced correction to Arrhenius law.

Nature communications·2024
Same author

Aging dynamics of d-dimensional locally activated random walks.

Physical review. E·2024
Same author

Leftward, rightward, and complete exit-time distributions of jump processes.

Physical review. E·2023
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles

Related Experiment Video

Updated: Jun 23, 2025

Non-invasive Assessments of Subjective and Objective Recovery Characteristics Following an Exhaustive Jump Protocol
08:21

Non-invasive Assessments of Subjective and Objective Recovery Characteristics Following an Exhaustive Jump Protocol

Published on: June 8, 2017

7.7K

Extreme value statistics of jump processes.

J Klinger1,2, R Voituriez1,2, O Bénichou1

  • 1Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne Université, 4 Place Jussieu, 75005 Paris, France.

Physical Review. E
|June 22, 2024
PubMed
Summary
This summary is machine-generated.

This study explores extreme value statistics for jump processes. We found key probabilities, like the semi-infinite propagator and strip probability, are crucial for understanding process extremes and their timing.

More Related Videos

Observation and Analysis of Blinking Surface-enhanced Raman Scattering
05:52

Observation and Analysis of Blinking Surface-enhanced Raman Scattering

Published on: January 11, 2018

7.4K
Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells
10:21

Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells

Published on: September 16, 2020

6.1K

Related Experiment Videos

Last Updated: Jun 23, 2025

Non-invasive Assessments of Subjective and Objective Recovery Characteristics Following an Exhaustive Jump Protocol
08:21

Non-invasive Assessments of Subjective and Objective Recovery Characteristics Following an Exhaustive Jump Protocol

Published on: June 8, 2017

7.7K
Observation and Analysis of Blinking Surface-enhanced Raman Scattering
05:52

Observation and Analysis of Blinking Surface-enhanced Raman Scattering

Published on: January 11, 2018

7.4K
Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells
10:21

Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells

Published on: September 16, 2020

6.1K

Area of Science:

  • Probability Theory
  • Stochastic Processes
  • Statistical Physics

Background:

  • Extreme value statistics (EVS) are critical for understanding rare events in complex systems.
  • Jump processes, characterized by discontinuous movements, are fundamental models in various scientific domains.
  • Analyzing the extremes of these processes requires specialized probabilistic tools.

Purpose of the Study:

  • To investigate extreme value statistics (EVS) for general discrete time and continuous space symmetric jump processes.
  • To identify key probabilistic quantities that govern the EVS of these processes.
  • To derive exact expressions and universal asymptotic behaviors for joint distributions of extremes and their associated times.

Main Methods:

  • For unbounded jump processes, the semi-infinite propagator G_{0}(x,n) was utilized.
  • For bounded, semi-infinite jump processes, the strip probability μ_{0,[under x]̲}(n) was introduced and analyzed.
  • Mathematical derivations were employed to obtain exact expressions and asymptotic behaviors of relevant distributions.

Main Results:

  • The semi-infinite propagator G_{0}(x,n) was shown to be essential for deriving joint distributions of extremes and their hitting times in unbounded jump processes.
  • The strip probability μ_{0,[under x]̲}(n) was identified as the fundamental quantity for analyzing EVS in bounded, semi-infinite jump processes.
  • Universal asymptotic behaviors for various joint distributions related to process extremes were extracted for both types of processes.

Conclusions:

  • The study provides a unified framework for analyzing extreme value statistics in a broad class of symmetric jump processes.
  • The identified key probabilistic quantities offer powerful tools for future research in extreme events.
  • The findings contribute to a deeper understanding of the behavior of stochastic systems at their extremes.