All Questions
Tagged with pr.probability markov-chains
362 questions
17
votes
2
answers
2k
views
Random walk is to diffusion as self-avoiding random walk is to ...?
One can view a random walk as a discrete process whose continuous
analog is diffusion.
For example, discretizing the heat diffusion equation
(in both time and space) leads to random walks.
Is there a ...
- 151k
4
votes
1
answer
383
views
initial condition of a diffusion approximation
I am trying to prove that a certain sequence of Markov chains $x^N_k$ converges towards a diffusion process. The invariant measure of $x^N$ is $\pi^N$ and the Markov chain $x^N$ is started in ...
- 2,133
7
votes
1
answer
296
views
Existence of Limiting Distribution for Moving Regions in Stat. Phys. Models
As the title (hopefully) suggests, I've been trying to prove (or disprove) the existence of a limiting distribution for a certain projection in a statistical physics model. I'll give the details of ...
- 101
2
votes
1
answer
543
views
"Induced" arrivals in an M/M/1 queue?
I'm a newcomer to the realm of queueing theory, so please bear with me :)
I'd like to model web server traffic with a modified M/M/1 queue.
In the simple case we have two parameters - $\lambda$ for ...
- 23
4
votes
1
answer
468
views
When is a 1-block factor of a non-Markovian process Markov?
Let $Y$ be a discrete stationary stochastic process. Suppose that $Y$ is not $n$-step Markov for any positive integer $n$. Let $Z$ be a 1-block factor of $Y$. For what condition on $Y$ or the ...
- 325
7
votes
2
answers
404
views
Examples of Slowly Mixing Chains in Statistics
This should probably be community wiki, but I don't know how to set that myself.
I'm looking for examples or Markov chains that are used in statistics or statistical physics, and which are known to ...
- 71
3
votes
1
answer
295
views
Finitarily Markovian Finite Factors of Bernoulli Schemes
By processes, I mean discrete, stationary stochastic processes, that is $(X,\mathcal{U},\mu,T)$ where $X$ is the set of doubly infinite sequences of some alphabet $A$, $\mathcal{U}$ is the $\sigma$-...
- 325
18
votes
4
answers
3k
views
Markov chain on groups
Let $G$ be a permutation group on the finite set $\Omega$. Consider the Markov chain where you start with an element $\alpha \in \Omega$ chosen from some arbitrary starting probability distribution. ...
- 85.6k
5
votes
2
answers
1k
views
Is there a way to analytically compute the recurrence time of a finite Markov process?
Let $X_t$ be an ergodic (time-homogeneous) Markov process (in discrete or continuous time) on a finite state space $\{1,\dots,n\}$. Let $T(X_0)$ be the stopping time given by the infimum of times such ...
- 15.4k
0
votes
1
answer
347
views
Where can I learn about master equation?
I am reading a paper by Dorogovstev on structure of growing complex networks with preferential linking. I need to learn master equation for this.
I need a reference for the same.
- 9
4
votes
1
answer
363
views
Efficiently sampling points from an integer lattice.
Let $\mathcal{L}$ = {x$\in$ $N^n$ : ||x||$_1$ $\leq$ m} denote the set of integer points in the positive orthant of the $\ell_1$ ball of radius $m$, where $m < n$. For each $x \in \mathcal{L}$, let ...
- 41
19
votes
9
answers
3k
views
How can I generate random permutations of [n] with k cycles, where k is much larger than log n?
I've been thinking a lot lately about random permutations. It's well-known that the mean and variance of the number of cycles of a permutation chosen uniformly at random from Sn are both ...
- 14k