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3
votes
1answer
310 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 ...
7
votes
1answer
231 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 ...
0
votes
0answers
231 views

Markov-chain alternative (from the perspective of “feedback”)

First of all, I'm not quiet sure the "feedback" word is used in this context. Let's say we have a simple M/M/1 queue. Markov-chains are used to describe such entities, for example taking the number of ...
2
votes
1answer
494 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 ...
4
votes
1answer
447 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 ...
6
votes
2answers
286 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 ...
3
votes
1answer
260 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 ...
12
votes
3answers
1k 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. ...
5
votes
2answers
597 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 ...
0
votes
1answer
305 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.
4
votes
2answers
276 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 ...
14
votes
9answers
2k 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 ...