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

Random Variables01:09

Random Variables

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...
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...
Shock Waves01:16

Shock Waves

While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the source's speed through it. When this condition is breached, a shock wave occurs.
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high pressures...
Randomized Experiments01:13

Randomized Experiments

The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
Simple...
Probability Distributions01:32

Probability Distributions

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 probability...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

You might also read

Related Articles

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

Sort by
Same author

Emergent Nonthermal Fluid from Jets in the Massive Schwinger Model Using Tensor Networks.

Physical review letters·2025
Same author

Nonorthogonal Eigenvectors, Fluctuation-Dissipation Relations, and Entropy Production.

Physical review letters·2025
Same author

Using space-filling curves and fractals to reveal spatial and temporal patterns in neuroimaging data.

Journal of neural engineering·2025
Same author

Scale-free correlations in the dynamics of a small (N∼10000) cortical network.

Physical review. E·2023
Same author

Eikonal formulation of large dynamical random matrix models.

Physical review. E·2021
Same author

Observing changes in human functioning during induced sleep deficiency and recovery periods.

PloS one·2021
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

Related Experiment Video

Updated: Jun 5, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Universal shocks in random matrix theory.

Jean-Paul Blaizot1, Maciej A Nowak

  • 1IPTh, CEA-Saclay, 91191 Gif-sur-Yvette, France. jean-paul.blaizot@cea.fr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

We connect universal kernels in random matrix theory to fluid dynamics shock formation. This reveals universal properties in both random matrix theory and Burgers equation solutions near shocks.

More Related Videos

2D and 3D Matrices to Study Linear Invadosome Formation and Activity
12:25

2D and 3D Matrices to Study Linear Invadosome Formation and Activity

Published on: June 2, 2017

Related Experiment Videos

Last Updated: Jun 5, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

2D and 3D Matrices to Study Linear Invadosome Formation and Activity
12:25

2D and 3D Matrices to Study Linear Invadosome Formation and Activity

Published on: June 2, 2017

Area of Science:

  • Mathematics
  • Physics
  • Fluid Dynamics

Background:

  • Random matrix theory (RMT) describes systems with many random components.
  • Fluid dynamical equations model fluid behavior.
  • Universality in RMT refers to properties independent of system details.

Purpose of the Study:

  • To link universal kernels in RMT to shock formation in fluid dynamics.
  • To explore the connection between RMT and Burgers equation dynamics.
  • To understand the universality at the spectrum edge in RMT.

Main Methods:

  • Deriving fluid dynamical equations from Dyson's random walks.
  • Rescaling time in Dyson's random walks.
  • Analyzing characteristic polynomials and their inverses for the Gaussian Unitary Ensemble (GUE).
  • Comparing RMT eigenvalue spectra to Burgers equation solutions.

Main Results:

  • Universal kernels in RMT are linked to shock formation in fluid dynamics.
  • Characteristic polynomials in GUE evolve via a viscous Burgers equation.
  • An effective spectral viscosity of ν(s)=1/2N was identified for matrix size N.
  • The RMT eigenvalue spectrum edge corresponds to the shock in the Burgers equation.

Conclusions:

  • A novel connection exists between RMT universality and fluid dynamics shock phenomena.
  • The Burgers equation provides a framework to understand RMT universality at the spectrum edge.
  • This work bridges concepts from statistical physics and continuum mechanics.