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

Absolute and Local Extreme Values01:22

Absolute and Local Extreme Values

The highest and lowest values of a function, relative to a reference axis, are known as extreme values. These include absolute maximum and absolute minimum values, which represent the highest and lowest points the function reaches across its entire domain. Within a restricted portion of the function, the highest and lowest values are referred to as local maximum and local minimum values, respectively.Periodic functions, such as sine and cosine, show extreme values at infinitely many points due...
Unusual Results01:16

Unusual Results

Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2σ  from the mean, μ  is considered unusual.
Maximum unusual value = μ + 2σ
Minimum unusual value...
Random Error01:04

Random Error

Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
Chebyshev's Theorem to Interpret Standard Deviation01:15

Chebyshev's Theorem to Interpret Standard Deviation

Chebyshev’s theorem, also known as Chebyshev’s Inequality, states that the proportion of values of a dataset for K standard deviation is calculated using the equation:
Regression Toward the Mean01:52

Regression Toward the Mean

Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when researchers try to extrapolate results...
Wald-Wolfowitz Runs Test II01:17

Wald-Wolfowitz Runs Test II

The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...

You might also read

Related Articles

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

Sort by
Same author

Proxitaxis: An adaptive search strategy based on proximity and stochastic resetting.

Physical review. E·2026
Same author

Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols.

Physical review. E·2026
Same author

Target Search Optimization by Threshold Resetting.

Physical review letters·2025
Same author

Enhanced diffusion over a periodic trap by hydrodynamic coupling to an elastic mode.

Communications physics·2025
Same author

Diffusion with stochastic resetting on a lattice.

Physical review. E·2025
Same author

Solving Lyapunov equations for electrically driven ternary electrolytes: Application to long-range van der Waals interactions.

Physical review. E·2025

Related Experiment Video

Updated: Jul 18, 2026

Longitudinal Measurement of Extracellular Matrix Rigidity in 3D Tumor Models Using Particle-tracking Microrheology
11:11

Longitudinal Measurement of Extracellular Matrix Rigidity in 3D Tumor Models Using Particle-tracking Microrheology

Published on: June 10, 2014

Large deviations of extreme eigenvalues of random matrices.

David S Dean1, Satya N Majumdar

  • 1Laboratoire de Physique Théorique (UMR 5152 du CNRS), Université Paul Sabatier, 118, Route de Narbonne, Toulouse Cedex 4, France.

Physical Review Letters
|December 13, 2006
PubMed
Summary

We analytically calculated large deviation probabilities for random matrix eigenvalues. The probability of all eigenvalues being positive decreases exponentially with matrix size N, revealing a universal exponent.

Related Experiment Videos

Last Updated: Jul 18, 2026

Longitudinal Measurement of Extracellular Matrix Rigidity in 3D Tumor Models Using Particle-tracking Microrheology
11:11

Longitudinal Measurement of Extracellular Matrix Rigidity in 3D Tumor Models Using Particle-tracking Microrheology

Published on: June 10, 2014

Area of Science:

  • Random matrix theory
  • Mathematical physics
  • Quantum chaos

Background:

  • The behavior of eigenvalues in random matrices is fundamental to understanding complex systems.
  • Previous studies focused on average properties, with less known about extreme eigenvalue distributions.

Purpose of the Study:

  • To analytically compute probabilities of large deviations for the largest/smallest eigenvalues in Gaussian ensembles.
  • To generalize the Wigner semicircle law for restricted eigenvalue distributions.

Main Methods:

  • Analytical calculations of eigenvalue distributions.
  • Analysis of large N behavior for random matrices.
  • Derivation of density of states for constrained eigenvalues.

Main Results:

  • Derived the probability of all eigenvalues being positive/negative, showing an exponential decay exp[-beta*theta(0)*N^2] for large N.
  • Identified a universal exponent theta(0) = (ln3)/4.
  • Calculated the average density of states, exhibiting an inverse square-root singularity at the eigenvalue threshold zeta.

Conclusions:

  • The study provides exact analytical results for rare eigenvalue events in random matrices.
  • The findings generalize the Wigner semicircle law and reveal universal properties of eigenvalue statistics.
  • The results have implications for fields relying on random matrix theory, such as quantum mechanics and statistics.