All Questions
14 questions
8
votes
1
answer
174
views
Equalizing Geometric means of Graph Cycles
Consider a strongly connected directed graph $G$. I have been stuck on the following question: can you assign real numbers in $[0,1]$ to each edge of $G$ so that the geometric mean of all cycles are ...
- 183
6
votes
1
answer
361
views
Random walks on infinite directed regular graphs
Let us consider a directed graph $\Gamma=(V,E,s,t)$ ($V$ set of vertices, $E$ set of edges, $s,t: E \rightarrow V$ are the "source" and "target" maps).
Assume that $\Gamma$ is bi-regular, that is ...
- 26k
4
votes
1
answer
587
views
Combinatorial descriptions of the stationary distribution of a Markov chain
When I say "Markov chain" I think of a directed positively weighted (finite) graph, such that the sum of all edges going out of a vertex equals 1. Also I assume that it is aperiodic and irreducible.
...
- 406
4
votes
3
answers
4k
views
Stationary distribution for bipartite graph
I was wondering if there is any stationary distribution for bipartite graph? Can we apply random walks on bipartite graph? since we know the stationary distribution can be found from Markov chain, but ...
- 51
3
votes
2
answers
1k
views
Non-backtracking random walk in regular (finite) graphs
I know that many things are known when dealing with random walks on a finite (or even infinite) graph: mixing time, returns to origin, etc. All is based in the use of the Markovian property of such a ...
- 1,561
3
votes
0
answers
151
views
Sequential generation of any random graph
The high-level question is: can we generate any random graph with size $d$ using a Markov chain?
For example, let $X^{(0)} = (1,0,\ldots,0) \in R^d$ be the initial state, and $X^{(t+1)} = f^{(t)}(X^{...
- 1,127
2
votes
1
answer
232
views
If the diameter of a bounded degree, directed graph is polynomial in the degree of the graph, is the mixing time also polynomial?
Given a directed graph $G=(V,E)$, with no self-loops, with a vertex that has a maximal out-degree $\le d\in O(\log |V|)$, and with a diameter $\text{diam}(G)\in O(\text{poly }d)$, consider converting ...
- 2,185
2
votes
0
answers
321
views
Why do we assume that $\mathcal{A}$ is an algebra in this 2003 paper of Bobkov and Tetali?
In Bobkov and Tetali - Modified Log-Sobolev Inequalities, Mixing and Hypercontractivity (extended version Modified Logarithmic Sobolev Inequalities in Discrete Settings), at the beginning of section 3,...
- 105
2
votes
0
answers
159
views
Distribution of path probabilities for a finite absorbing Markov chain
I am interested in the distribution of path probabilities for a finite
absorbing (but otherwise well behaved) Markov chain. Has this topic
been considered in the literature?
A bit of Googling ...
- 15.4k
1
vote
1
answer
242
views
Two types of random walkers on square lattice
Consider a two dimensional square lattice ($n$ by $n$), which is our space $S$ (each point labelled by an index $1\to n^2$), containing two types of particles, distinguished here by either an index $1$...
user82424
1
vote
1
answer
295
views
Equivalent Markov Random Fields
Hi,
Is it possible to have topologically different Markov Random Fields (few different edges) and yet yielding the same inference results ?
Thanks!
- 167
1
vote
0
answers
41
views
Asymptotic mixing time and Euclidean probability distance for path graphs
We are given a simple path graph $P(V,E)$ with vertex set $V$ and edge set $E$, having $n=|V|$ nodes. Given an initial distribution $\mathbf{\mu}$ over $V$, let $d_t(\mathbf{\mu},\pi)$ be defined as $\...
- 1,677
1
vote
0
answers
46
views
Is there an effective algorithm for finding "minimal discovery times" for large graphs?
Consider a large, probably sparse graph with Markovian random walkers on it.
Define the discovery time as the expected time to first reach a vertex by
random walk from a uniform start. Are there ...
- 355
-2
votes
1
answer
181
views
Stationary distribution of a weighted directed acyclic graph
Is there any way to calculate the equilibrium (stationary) distribution for a weighted directed acyclic graph?
Some references emphasized adjacency matrix to be symmetric.
https://arxiv.org/abs/1012....
