2
votes
0answers
28 views

Dhar's Burning Test - Confusion about Abelian Sandpile Model

Dhar's Burning test is a bijection between the spanning trees of a certain graph and the recurrent states Abelian sandpile model. I would like some help working out this bijection in different cases: ...
0
votes
0answers
58 views

Derivative of student's t with respect to degree of freedom.

I would like to show that $\Big(1+\frac{\Psi_\delta^{-1}(\rho)^2}{\delta}\Big)^{-\frac{\delta}{2}+\frac{1}{2}}$ decreases in $\delta$, where $\Psi^{-1}_\delta(\cdot)$ is the inverse CDF of a student's ...
1
vote
1answer
51 views

The Average Speed of an object

I'm pretty sure this has more to do with fundamental Math than Physics and that is why I'm asking this here rather than Physics.SE Imagine some object travelling along a straight path from point $A$ ...
5
votes
0answers
45 views

Deconvolution of distribution of diffraction reflexes

I'm a chemist stuck in a mathematical problem. Please bear with me as I'm trying to express myself in Math language. Let me explain in short terms the experimental method I'm using: X-ray ...
0
votes
1answer
37 views

distribution of the product of a poisson and a bolzmann

What is the distribution of the product of two variables for which each of them has its own distribution(specifically one poisson and one bolzmann)? I found on wikipedia that for the sum of the two ...
1
vote
1answer
378 views

Describe a sine wave of known frequency with only two points

This is my first post on math.stackexchange (sorry if meta people remove the Hello (sometimes we do that over on stackoverflow ;P)! I have a system wherein I know that the output is a sine wave, with ...
3
votes
0answers
85 views

Who established the word “ Degree of freedom ” in statistics?

I wonder who is the first one that established and applied the word : "degree of freedom" in statistics? Why he/she need degree of freedom in the calculation of many statistical values?
0
votes
1answer
27 views

Basic expression mangling question

I am looking at the solution of a physics/statistics hybrid exercise, and I can't figure out how one expression step took place. I have that $${dx \over dt} = gt$$ $$T = \sqrt{2h \over g}$$ where ...
1
vote
0answers
64 views

Stochasticity of Fermi problems

The great physicist Enrico Fermi was known for his ability to make good guesses with little or bad data by multiplying series of estimates. 1 I've seen this described as corresponding to a stochastic ...
3
votes
1answer
228 views

dynamic mean: measurement of randomly distributed events

Aim is to estimate an error on a stochastic event rate. I read out the event counter second-wise, every black $1$ is a counted event (new events over time, see the plot below). During the measurement ...
4
votes
1answer
276 views

Fourier (Hankel?) transform of a discrete set of radial points (question from a chemist!)

I'm sorry because I'm not a mathematician so that my question may look a little bit messy. I have tabulated values [1] of a 3 dimensional radial function $f(r)$: ...
9
votes
2answers
627 views

What is the relationship between the Boltzmann distribution and information theory?

I'm reading a paper on Boltzmann machines (a type of neural network in Machine Learning), and it mentions that "The Boltzmann distribution has some beautiful mathematical properties and it is ...
3
votes
3answers
803 views

The relationship between mean and variance in the context of system energy and the partition function

I'm looking at a specific derivation on wikipedia relevant to statistical mechanics and I don't understand a step. $$ Z = \sum_s{e^{-\beta E_s}} $$ $Z$ (the partition function) encodes information ...
2
votes
3answers
2k views

Probability concerning unfair dice with N sides

Fair warning: I am not a math expert (that's why I'm here). I would like to be able to calculate the probability of rolling a certain side on a die with n sides where any number of those sides has an ...