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Decus in Labore

The Quantum Ergodicity Theorem. Of Shnirelman, Colin de Verdière and Zelditch is a result that combines in a nice way several different concepts. Namely, suppose. Is a compact Riemannian manifold with ergodic geodesic flow. Let. Be the appropriately normalized eigenfunctions of the Laplacian. Then the measures with density. Tend weakly to the usual volume. I am following a series of lectures notes due to Faure and Anantharaman available here. Continue reading →. February 28, 2016. Steps, consider the pro...

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Decus in Labore | decusinlabore.wordpress.com Reviews
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The Quantum Ergodicity Theorem. Of Shnirelman, Colin de Verdière and Zelditch is a result that combines in a nice way several different concepts. Namely, suppose. Is a compact Riemannian manifold with ergodic geodesic flow. Let. Be the appropriately normalized eigenfunctions of the Laplacian. Then the measures with density. Tend weakly to the usual volume. I am following a series of lectures notes due to Faure and Anantharaman available here. Continue reading →. February 28, 2016. Steps, consider the pro...
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Decus in Labore | decusinlabore.wordpress.com Reviews

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The Quantum Ergodicity Theorem. Of Shnirelman, Colin de Verdière and Zelditch is a result that combines in a nice way several different concepts. Namely, suppose. Is a compact Riemannian manifold with ergodic geodesic flow. Let. Be the appropriately normalized eigenfunctions of the Laplacian. Then the measures with density. Tend weakly to the usual volume. I am following a series of lectures notes due to Faure and Anantharaman available here. Continue reading →. February 28, 2016. Steps, consider the pro...

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Torsion on Jacobians and Teichmuller dynamics – Decus in Labore

https://decusinlabore.wordpress.com/2014/01/03/torsion-on-jacobians-and-teichmuller-dynamics

Torsion on Jacobians and Teichmuller dynamics. In this post, I will describe a special case of a theorem about torsion points on Jacobians and Teichmuller dynamics which is proved in this paper. Namely, I will describe a different proof of a theorem of Moeller. That for Teichmuller curves, zeroes of the holomorphic. Form must land in the torsion of (a factor of) the Jacobian. Some familiarity with Teichmuller dynamics will be assumed, as in the survey of Zorich. Mdash; 1. Setup —. We only have the. To pr...

2

Quantum Ergodicity – Decus in Labore

https://decusinlabore.wordpress.com/2016/02/28/quantum-ergodicity

The Quantum Ergodicity Theorem. Of Shnirelman, Colin de Verdière and Zelditch is a result that combines in a nice way several different concepts. Namely, suppose. Is a compact Riemannian manifold with ergodic geodesic flow. Let. Be the appropriately normalized eigenfunctions of the Laplacian. Then the measures with density. Tend weakly to the usual volume. I am following a series of lectures notes due to Faure and Anantharaman available here. Fix the following notation for the rest of the post:. Basic pr...

3

Root systems – Decus in Labore

https://decusinlabore.wordpress.com/2014/09/10/root-systems

In this post, I will record some properties of reduced root systems, following Bourbaki. The reference is their “Lie groups and algebras, Ch. 4-6”. There will be no proofs, just a summary of the main properties. The post consists mainly of definitions and lists their properties. Throughout, all root systems are assumed reduced. Is the data of a real vector space. Of roots such that. Is finite and generates. Ii) The group generated by the. Is called the Weyl group of. The dual root system, and. In the usu...

4

Entropy and set projections – Decus in Labore

https://decusinlabore.wordpress.com/2014/09/11/entropy-and-set-projections

Entropy and set projections. Be a finite set, and let. Be its projections to the corresponding two-planes. Denoting by. The cardinality of a set. We have the following inequality:. This generalizes to sets in higher dimensions and projections to subspaces of possibly different dimensions. As long as each coordinate appears at least. Times on the right, the size of. Is bounded by the product of the projections. Functions of two variables, we have. To be indicators of projections of. Mdash; Entropy —.

5

Large Deviations – Cramer’s theorem – Decus in Labore

https://decusinlabore.wordpress.com/2015/10/24/large-deviations-cramers-theorem

Large Deviations – Cramer’s theorem. Last summer I attended a conference on “Dynamics and Numbers” at the Max Planck Institute in Bonn. Vincent Delecroix gave a nice talk on large deviations for the Teichmuller flow, and I decided to learn a bit about this concept. I wrote the notes below at that time. In this post, I will prove the simplest example of large deviations – Cramer’s theorem. Here is a simple example. Consider a random coin toss, and at each step you either win or loose. With this law and let.

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A pinching and twisting monoid of symplectic matrices which is not Zariski dense in the full symplectic group | Disquisitiones Mathematicae

https://matheuscmss.wordpress.com/2015/07/17/a-pinching-and-twisting-monoid-of-symplectic-matrices-which-is-not-zariski-dense-in-the-full-symplectic-group

July 17, 2015. A pinching and twisting monoid of symplectic matrices which is not Zariski dense in the full symplectic group. Consider a random product of two symplectic matrices. On a real symplectic vector space. That is, the (symplectic). Is the shift map equipped with the Bernoulli measure. By Oseledets multiplicative ergodic theorem. The Lyapunov exponents of the random product of. Ie, the linear cocycle. Describing the exponential growth of the singular values of the random products. Of course, the...

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Sur le cocycle de Kontsevich-Zorich au-dessus de deux origamis spéciaux (slides of a talk in Orsay) | Disquisitiones Mathematicae

https://matheuscmss.wordpress.com/2009/05/04/sur-le-cocycle-de-kontsevich-zorich-au-dessus-de-deux-origamis-speciaux-slides-of-a-talk-in-orsay

May 4, 2009. Sur le cocycle de Kontsevich-Zorich au-dessus de deux origamis spéciaux (slides of a talk in Orsay). Firstly, let me apologize for the 1 month and half hiatus: while I plan to close up my series on the talks and courses of the Dynamical Systems conference (held at ICTP, Italy), I wasn’t able to do so during April because I was learning some interesting facts about square-tiled surfaces and Teichmuller dynamics from my new friends Pascal Hubert. Invariant ergodic probability is. Ie, all expon...

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Hausdorff dimension of the graphs of the classical Weierstrass functions (after Weixiao Shen) | Disquisitiones Mathematicae

https://matheuscmss.wordpress.com/2015/06/30/hausdorff-dimension-of-the-graphs-of-the-classical-weierstrass-functions-after-weixiao-shen

June 30, 2015. Hausdorff dimension of the graphs of the classical Weierstrass functions (after Weixiao Shen). About two weeks ago, Weixiao Shen gave the talk “. Hausdorff dimension of the graphs of the classical Weierstrass functions. 8221; during the Third Palis-Balzan International Symposium on Dynamical Systems. In the sequel, I will transcript my notes from Shen’s talk. In Real Analysis, the classical Weierstrass function. Note that the Weierstrass functions have the form. Weierstrass (1872) and Hardy.

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Decus in Labore

The Quantum Ergodicity Theorem. Of Shnirelman, Colin de Verdière and Zelditch is a result that combines in a nice way several different concepts. Namely, suppose. Is a compact Riemannian manifold with ergodic geodesic flow. Let. Be the appropriately normalized eigenfunctions of the Laplacian. Then the measures with density. Tend weakly to the usual volume. I am following a series of lectures notes due to Faure and Anantharaman available here. Continue reading →. February 28, 2016. Steps, consider the pro...

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