All Questions
13 questions
2
votes
2
answers
167
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
0
votes
1
answer
77
views
Reference request: $\mathbb{E}|X_t| \to \infty$ as $t \to \infty$ when $\{X_t\}_{t\geq 0}$ is a continuous-time (symmetric) random walk
Let $\{X_t\}_{t\geq 0}$ be a one dimensional continuous-time (symmetric) random walk on $\mathbb Z$ defined via $$X_t = X_0 + \sum_{i=1}^{N_t} Y_i,$$ where $X_0 \in \mathbb{Z}_+$ is a non-negative ...
- 730
3
votes
2
answers
478
views
Random spanning trees probability problem
We are given a simple connected graph $G(V,E)$ with vertex and edge set $V$ and $E$ respectively. For any vertex $v\in V$, let $D_T(v)$ the degree of $v$ in a uniformly generated random spanning tree $...
- 1,677
1
vote
1
answer
425
views
Invariance principle: Brownian bridge and random walk conditioned on end point
Let $\{X_i, i \in \mathbb{N}\}$ be a sequence of non-lattice i.i.d. centered random variables, $\mathbb{E} |X_1| ^3 < 0$. Let $S_n = \sum\limits _{i=1} ^n X_i$ be the corresponding random walk and ...
- 724
1
vote
0
answers
91
views
A random process with conserved momentum: 'particle decay'?
Consider a particle $p_1$ moving at unit speed along a straight line in $\mathbf{R}^2$, directed by some vector $v_1 \in \mathbf{S}^1$. Equid this particle with a Poisson clock $\tau_1$, with ...
- 5,038
4
votes
2
answers
480
views
Hitting probability of a line
Consider a simple (nearest neighbor) random walk on a lattice $\Bbb Z^2$ which starts at the origin, is constrained to $x\ge 0$ halfplane, and stops when it hits the line $x=n$. Denote by $p(n,k)$ ...
- 17k
0
votes
2
answers
266
views
Last crossing of a line by a random walk
Let $X_1, X_2, ...$ be i.i.d. random variables, $\mathbb{E} X_1 > 0$, and let $S_n = \sum\limits _{i = 1} ^n X_i$. Define $\tau = \max \{n \in \mathbb{N}: S_n \leq 0 \}$ with the convention $\tau =...
- 724
2
votes
0
answers
63
views
hitting probabilities of oriented random walk
Consider a random walk on $\mathbb{Z}^2$, starting at $(0,0)$. Each step it moves rightwards with probability $p$ and upwards with probability $q=1-p$. The random walk terminates when it hits the ...
- 640
4
votes
1
answer
176
views
Random Walk with "Forward Dependency"
Let $\{X_t\}_{t=-\infty}^{\infty}$ be a sequence of random variables. We are interested in a "random walk" (or more generally, a random field) that can be characterized by
$$
X_t ~|~ X_{t-k}, \ldots, ...
- 1,127
1
vote
0
answers
60
views
Probability for a SRW to be at some place in an even number of steps
I am looking for some references for the following problem.
Consider a graph $G$ and a simple continuous time random walk $(X_t)_{t\geqslant 0}$ on this graph. Consider the family of events $(e_t)_{t\...
- 166
1
vote
0
answers
365
views
Diagonal of Green's Function
I am looking to numerically calulate the diagonal of Green's function. I am interested in Green's functions of elliptic PDEs and in those that arise from stochastic processes (discrete and continuous)....
- 185
9
votes
1
answer
488
views
Mixing time of unitary Brownian motion
Let $B_t$ be the unitary Brownian motion, i.e. Brownian motion on the unitary group $U(N)$. What is known about the mixing time of $B_t$, that is, how fast does the measure $B_t(\delta_{\{Id\}})$ ...
- 3,323
0
votes
2
answers
3k
views
Two dimensional brownian motion first passage time
Hello,
I am looking for information on how to solve/compute first passage time for two dimensional Brownian motion.
any papers, references, books or web links for study will be helpful.
thanks
...
- 21