All Questions
8 questions
2
votes
2
answers
165
views
Example of random walk in a random environment (RWRE) saying things on the environment
I was wondering if anyone is aware of works/articles/examples where random walks in a random environment (RWRE) are actually used for obtaining information on the random environment.
To clarify a bit, ...
- 59
2
votes
2
answers
183
views
Which infinite random graphs with percolation threshold $p_c=0$ are transient?
I am interested in long-range percolation models with heavy-tailed degree distributions such as DHH13, GLM21, Y6. The simplest example is scale-free percolation in which vertices are elements $\mathbb{...
2
votes
1
answer
900
views
Asymptotically tight concentration of norms of subgaussian random vectors with independent coordinates, as the dimension $n \to \infty?$
Let $X=(X_1 \dots X_n)\in \mathbb{R}^n,$ be a subgaussian random vector so that $X_i$'s are independent, $\mathbb{E}X_i = 0, \mathbb{E}X_i^2=1.$ Before we pose our question, let's state the following:
...
- 1,465
2
votes
1
answer
238
views
On lower bounds for harmonic functions on $\mathbb{Z}^d$
Consider a non-constant harmonic function $f$ on $\mathbb{Z}^d$ (meaning this that $f(x)$ if the average of the $2d$ values $f(y)$ such that the distance between $x$ and $y$ is one). Let $M_n$ denote ...
- 153
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
168
views
Random Walk 2D with dependent weights [closed]
I have spent a lot of time trying to solve this problem but have had no luck so far! Any help would be highly appreciated!
Suppose I have a 3x3 grid as shown below.
(3,1) (3,2) (3,3)
(2,1) (2,2) (...
- 23
4
votes
0
answers
158
views
Using Crump-Mode-Jagers processes to get logarithmic bound on a random tree height
I am currently pursuing my PhD degree and in my research I came across a family of random trees. I need to prove a logarithmic asymptotic bound for the heights of such trees as their size grows. I ...
- 41
5
votes
1
answer
1k
views
Self Avoiding Walk Enumerations
Let $c(n)$ be the number of Self avoiding walks (SAW) of length $n$ on an infinite lattice $L$. Are there any known non-geometric interpretations of $c(n)$?. For example, is there a number theoretic ...
- 4,952