This page is the root of the EVOL Project encyclopedia. This mini-encyclopedia looks like an oriented graph of small articles about various aspects of the scientific content of the EVOL project. For the moment, it is an experimental part of this website.

This encyclopedia works like Wikipedia (see below for more informations on how to contribute). Unlike Wikipedia or other wikis containing mathematics, this encyclopedia is at the research level. Also, an article in the encyclopedia may contain potentially open questions and many unpublished remarks of interest.

The primary medium term objective of this mini-encyclopedia is to provide an original view of the EVOL project and to promote the diffusion of information inside and outside EVOL. Contributions by other people from the scientific community are welcome (see below for more explanations on how to contribute). In case of success, the encyclopedia might survive to the EVOL Project period (2009-2011) and might constitute an open collaborative scientific website.

Contents

  1. Some encyclopedia articles by keywords
    1. Criteria
    2. Equations
    3. Inequalities
    4. Formulas
    5. Groups
    6. Models
    7. Sobolev
    8. Gross
  2. Full alphabetical list of encyclopedia articles
  3. How to contribute to the encyclopedia
    1. Account creation and write access activation
    2. How to create a new article
    3. How to find a list of missing pages
    4. How to type in LaTeX formulas
  4. Encyclopedia team
  5. External links to other wikis with mathematical content
  6. Copyright and license

Some encyclopedia articles by keywords

1. Criteria

  1. Curvature-dimension criterion
  2. Hardy criterion
  3. Hörmander condition (criterion)
  4. Integral criteria
  5. Lyapunov condition (criterion)

2. Equations

  1. Boltzmann equation
  2. Chapman-Kolmogorov equation
  3. Fokker-Planck equation
  4. Granular medium equation
  5. Hamilton-Jacobi equation
  6. Heat equation
  7. Ornstein-Uhlenbeck equation
  8. Porous medium equation
  9. Reaction-diffusion equation
  10. Schrödinger equation

3. Inequalities

  1. Beckner inequality
  2. Brunn-Minkowski inequality
  3. Capacity-measure inequality
  4. Concentration inequality
  5. Entropy-energy inequality
  6. Euclidean logarithmic Sobolev inequality
  7. Fractional logarithmic Sobolev inequality
  8. Gagliardo-Nirenberg inequality
  9. Gaussian concentration inequality
  10. Hardy inequality
  11. L^q-logarithmic Sobolev inequality
  12. Li-Yau inequality
  13. Local Phi-entropy inequality
  14. Logarithmic Sobolev inequality
  15. Modified logarithmic Sobolev inequality
  16. Phi-entropy inequality
  17. Poincaré inequality
  18. Prékopa-Leindler inequality
  19. Sobolev inequality
  20. Super Poincaré inequality
  21. Transportation inequality
  22. Weak Poincaré inequality
  23. Weak logarithmic Sobolev inequality

4. Formulas

  1. Feynman-Kac formula

5. Groups

  1. Carnot groups
  2. Heisenberg group
  3. Lie groups
  4. Markov semigroup

6. Models

  1. Heat bath model
  2. Keller-Siegel model
  3. Persistent turning walker model
  4. TCP window size model
  5. Wright-Fisher model

7. Sobolev

  1. Euclidean logarithmic Sobolev inequality
  2. Fractional logarithmic Sobolev inequality
  3. L^q-logarithmic Sobolev inequality
  4. Logarithmic Sobolev inequality
  5. Logarithmic Sobolev via capacity-measure
  6. Modified logarithmic Sobolev inequality
  7. Sobolev inequality
  8. Weak logarithmic Sobolev inequality

8. Gross

  1. Hypercontractivity
  2. Lie groups
  3. Logarithmic Sobolev inequality
  4. Phi-entropy inequality

Full alphabetical list of encyclopedia articles

  1. Beckner inequality
  2. Boltzmann equation
  3. Brunn-Minkowski inequality
  4. Capacity-measure inequality
  5. Carnot groups
  6. Chapman-Kolmogorov equation
  7. Concentration inequality
  8. Curvature-dimension criterion
  9. EncyclopediaTemplate
  10. Entropic convergence
  11. Entropy-energy inequality
  12. Ergodicity
  13. Euclidean logarithmic Sobolev inequality
  14. Feynman-Kac formula
  15. Fokker-Planck equation
  16. Fractional logarithmic Sobolev inequality
  17. Fractional operator
  18. Gagliardo-Nirenberg inequality
  19. Gaussian concentration inequality
  20. Gradient flow
  21. Granular medium equation
  22. Hamilton-Jacobi equation
  23. Hardy criterion
  24. Hardy inequality
  25. Heat bath model
  26. Heat equation
  27. Heat kernel
  28. Heisenberg group
  29. Hypercontractivity
  30. Hypocoercivity
  31. Hypoellipticity
  32. Hörmander condition (criterion)
  33. Integral criteria
  34. Keller-Siegel model
  35. L^q-Poincaré
  36. L^q-logarithmic Sobolev inequality
  37. Li-Yau inequality
  38. Lie groups
  39. Local Phi-entropy inequality
  40. Logarithmic Sobolev inequality
  41. Logarithmic Sobolev via capacity-measure
  42. Lyapunov condition (criterion)
  43. Lévy operator
  44. Markov semigroup
  45. Mass transportation method
  46. Modified logarithmic Sobolev inequality
  47. Ornstein-Uhlenbeck equation
  48. Persistent turning walker model
  49. Phi-entropy inequality
  50. Poincaré inequality
  51. Poincaré via Lyapunov
  52. Poincaré via capacity-measure
  53. Porous medium equation
  54. Prékopa-Leindler inequality
  55. Reaction-diffusion equation
  56. Schrödinger equation
  57. Sobolev inequality
  58. Super Poincaré inequality
  59. TCP window size model
  60. Transportation inequality
  61. Wasserstein distance
  62. Weak Poincaré inequality
  63. Weak logarithmic Sobolev inequality
  64. Wright-Fisher model

How to contribute to the encyclopedia

To modify or create an article in the encyclopedia, you need an account with write access.

1. Account creation and write access activation

You may create your own account by using the menu (left top of this page). The encyclopedia team will be then notified by your account creation. You must then wait for the approval of your write access. This may take some few days.

2. How to create a new article

First of all, you must check that the article does not exists in the encyclopedia. You can use for that the list above or the Search box (right top corner of this page). To create a new article, you can either

Your new article will automatically appear in the encyclopedia articles list above.

3. How to find a list of missing pages

You may try WantedPages. See also SiteNavigation.

4. How to type in LaTeX formulas

During article editions, you can type your LaTeX formulas directly into the on-line editor. The wiki engine will automatically invoque a LaTeX engine, will convert the DVI into a PNG image, and will display it for you. For instance, you may write $e^{i\pi}=-1$ or the displaystyle version

$$e^{i\pi}=-1.$$

Here are other examples: The Gaussian distribution and the Mehler formula for the Ornstein-Uhlenbeck process:

$$ \sqrt{2\pi} =\int_{-\infty}^{+\infty} \exp\left(-\frac{1}{2}x^2\right) dx \quad\text{and}\quad P_t(f)(x)=(2\pi)^{-d/2}\int_{\mathbb{R}^d}\!f(xe^{-t}+\sqrt{1-e^{-2t}}\,y)\,e^{-|y|^2/2}\,dy $$

Encyclopedia team

The encyclopedia team keeps things working in the right way. Present team members are

The team is responsible for the editorial policy and for the global coherence of the projet.

External links to other wikis with mathematical content

Copyright and license

As for Wikipedia, all text in the EVOL project encyclopedia is available under the terms of the GNU Free Documentation License. See Copyrights for details.

CategoryEncyclopedia (last edited 2008-12-11 20:28:25 by DjalilChafai)