Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Standard Deviation of Calculated Results

Standard Deviation of Calculated Results

Standard deviation measures the spread of data around the mean value. Many large data sets follow a Gaussian distribution, also known as a normal distribution. This distribution is bell-shaped curved, with the most frequently observed value (mean or central value) in the middle. The farther away from the central value, the greater the deviation from the central value, and the lower the frequency.
A broad Gaussian distribution curve has a wider standard deviation, representing a data set with...

Empirical Method to Interpret Standard Deviation

Empirical Method to Interpret Standard Deviation

The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...

Coefficient of Variation

Coefficient of Variation

The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can compare two data series with drastically different means or different units of measurement. The coefficient of variation for a sample and a population is expressed as a percentage of the ratio of standard deviation to the mean.
The coefficient of variation is a practical statistical tool in finance. It allows investors to assess the volatility or...

P-value

P-value

P-value is one of the most crucial concepts in statistics.
P-value stands for the probability value. P-value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.
A large P-value calculated from the data indicates to not reject the null hypothesis. But a higher P-value does not mean that the null hypothesis is true. The smaller the P-value, the more unlikely...

Standard Error of the Mean

Standard Error of the Mean

The sampling variability of a statistic is defined as how much the statistic varies from one sample to another. The sampling variability of a statistic is typically measured by measuring its standard error.The standard error of the mean is an example of a standard error. It is a unique standard deviation known as the standard deviation of the sampling distribution of the mean. The standard error of the mean is a statistic that calculates how correctly a sample distribution represents a...

Expected Value

Expected Value

The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:In the equation, x is an event, and P(x) is the probability of the event occurring.The expected value has practical applications in decision theory.This text is adapted from Openstax, Introductory Statistics, Section 4.2 Mean or Expected Value and...

You might also read

Related Articles

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

Sort by

Same author

Comment on "Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices".

Physical review. E·2019

Same author

Vicious walks with a wall, noncolliding meanders, and chiral and Bogoliubov-de Gennes random matrices.

Physical review. E, Statistical, nonlinear, and soft matter physics·2003

See all related articles

Search research articles

Related Experiment Video

Updated: Jul 11, 2026

Comprehensive Workflow for the Genome-wide Identification and Expression Meta-analysis of the ATL E3 Ubiquitin Ligase Gene Family in Grapevine

Comprehensive Workflow for the Genome-wide Identification and Expression Meta-analysis of the ATL E3 Ubiquitin Ligase Gene Family in Grapevine

Published on: December 22, 2017

Eigenvalue statistics of the real Ginibre ensemble.

Peter J Forrester¹, Taro Nagao

¹Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia.

Physical Review Letters

|October 13, 2007

Summary

Researchers analyzed random matrices from the Ginibre ensemble, deriving formulas for eigenvalue correlations. This work provides a method to calculate the probability density of the largest real eigenvalue, relevant for biological web stability.

More Related Videos

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

Published on: September 21, 2017

Digital PCR-based Competitive Index for High-throughput Analysis of Fitness in Salmonella

Digital PCR-based Competitive Index for High-throughput Analysis of Fitness in Salmonella

Published on: May 13, 2019

Related Experiment Videos

Last Updated: Jul 11, 2026

Comprehensive Workflow for the Genome-wide Identification and Expression Meta-analysis of the ATL E3 Ubiquitin Ligase Gene Family in Grapevine

Comprehensive Workflow for the Genome-wide Identification and Expression Meta-analysis of the ATL E3 Ubiquitin Ligase Gene Family in Grapevine

Published on: December 22, 2017

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

Published on: September 21, 2017

Digital PCR-based Competitive Index for High-throughput Analysis of Fitness in Salmonella

Digital PCR-based Competitive Index for High-throughput Analysis of Fitness in Salmonella

Published on: May 13, 2019

Area of Science:

Mathematics
Probability Theory
Random Matrix Theory

Background:

The Ginibre ensemble is a set of random N x N matrices with independent and identically distributed standard Gaussian entries.
Understanding eigenvalue distributions in random matrices is crucial for various scientific fields.

Purpose of the Study:

To derive general n-point correlation functions for real and complex eigenvalues of the real Ginibre ensemble.
To develop a computationally tractable formula for the cumulative probability density of the largest real eigenvalue.

Main Methods:

Utilizing the method of skew orthogonal polynomials.
Expressing correlations as n x n Pfaffians with explicit entries.

Main Results:

General n-point correlation functions for real and complex eigenvalues were obtained.
A computationally tractable formula for the cumulative probability density of the largest real eigenvalue was derived.

Conclusions:

The derived formulas provide a deeper understanding of the statistical properties of the Ginibre ensemble.
The results are applicable to stability analysis in complex systems, such as biological webs, as per May's work.