Assume is an Gaussian matrix, i.e., its entries are i.i.d. standard normal random variables, with . Take for some fixed real scalars. I am interested in finding the p.d.f. of the "unitary" matrix from the QR decomp...

So if I write the action for a gas:

where is the kinetic energy and is potential energy.

I suspect there is a constant term (which does not affect the equations of motion) for the gas (in classical mechanic...

Let be the standard one-dimensional Cauchy distribution, i.e.

\begin{align} \mu_0 (dx) = \frac{1}{\pi} \frac{1}{1+x^2} dx. \end{align}

Suppose I fix , and form a Markov chain as follows:

1. At step , I sample .
2. I the...

Cell proliferation and cell diffusion seem to be important quantities to estimate when trying to understand or measure tumor growth, but I don't really understand a) the difference between them or b) their relationship to tumor growth.

Cell proliferation refers to cellular subdivision. This doesn'...

In Souslin trees on the first inaccessible cardinal it is asked if it is consistent that there are no Souslin trees at the least inaccessible cardinal .

In this question I would like to as...

Let be the category of finite sets.

A finite set structure is a faithful functor such that, for any , there are only finitely many isomorphism classes of objects maps to .

Question. Is there a natural finite s...

It's straightforward to prove that , which furthermore allows us to use the Gelfond-Schneider theorem to prove that .

Is it true that ?

It seems like it ought to be true, though my guess would be that this is an open proble...

In eusocial animals for which hearing is important to communicate between individuals, is there any species apart humans for which there are some evidence that the group adapts their acoustic communication to a fully or partially deaf individual of the group?

For instance, by systematically vocaliz...

Let and be random vectors defined on a common probability space. takes values in a finite-dimensional space , while takes values in . The conditional expectation is then a random variable that is uniquely defined up to null ...

I have a type of minimization problem I frequently solve that involves warping a large 2D triangle-mesh (~25,000 vertices) to fit a model. In the mesh, vertices carry the empirical measurements (each of which has a predicted position in the model, which is a continuous field). The potential/objectiv...

In this text, the author says (well, he says it in French, but I am too lazy to fix all the accents, so here is a Google translation):

_In any case, contemporary mathematics provides an example of extraordinarily deep and highly s...