# Tagged Questions

**7**

votes

**1**answer

131 views

### Trapping a particle

A particle starts a brownian walk in the middle of a long tunnel in the plane, at one end of the tunnel is a circular region X, at the other end a region Y of given area A.
Does the shape of region ...

**41**

votes

**5**answers

3k views

### Escape the zombie apocalypse

Consider zombies placed uniformly at random over $\mathbb{R}^2$ with asymptotic density $\mu$ zombies/area. You are placed at a random point and can move with speed $1$. Zombies move with speed $v\leq ...

**2**

votes

**1**answer

300 views

### Dynamics of Master Equation

I'm going to do research on dynamics of master equation of $n$ states
$$\dot p_i=A_{ij}p_j\qquad i=1\ldots n$$
where $p_i$ is the $i$-th component of probability vector and $A_{ij}$ is transition rate ...

**1**

vote

**0**answers

105 views

### Langevin equation with position-dependant damping: existence of an invariant measure?

The usual Langevin equation for a particle in a 1D harmonic potential
$dq(t) = p(t)~dt$
$dp(t) = -q(t)~dt + a ~dW(t) - b~p(t)~dt$
admits as an invariant measure the Gibbs measure ${1\over ...

**1**

vote

**0**answers

111 views

### Adding a damping term to a dynamical system or Markov process: what happens to invariant measures?

Consider the continuous-time Markov process on ${\mathbb R}^n$ described by the SDE
$\dot{x}(t) = F(x(t)) + \xi(t)$
where $F:{\mathbb R}^n \to {\mathbb R}^n$ is a smooth mapping, and $\xi(t)$ is a ...

**5**

votes

**2**answers

216 views

### Liverani's CLT (a question)

Let $(\Omega,\mathcal{F},P)$ be a probability space where $\Omega$ is a complete separable metric space, let $T:\Omega\to \Omega$ ` be an ergodic transformation, let $\hat{T}:L^{2}_{_P}(\Omega)\to ...

**2**

votes

**2**answers

490 views

### Midpoint lattice polygons

Midpoint polygons (a.k.a Kasner polygons) have been studied, and their behavior is well understood.
I am considering a variant, which I call midpoint lattice polygons.
Start with a sequence of ...