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Results tagged with random-walks
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user 420641
1
vote
1
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381
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Reference: probability distribution of first meeting time of two random walks on a cycle graph
I am looking for a reference or derivation for the following question:
Consider a cycle graph $G$ with $N$ vertices (see example here). Let two independent continuous-time random walkers$^\star$ start …
- 274
0
votes
1
answer
56
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Probability of random walk on confined lattice with reflective boundaries
Consider a simple random walk in one dimension with reflective boundaries at $n=1$ and $n=N$. We can express it via the master equation:
\begin{equation}
P(n,t) = \frac{1}{2}P(n-1,t-1) + \frac{1}{2}P( …
- 274
1
vote
1
answer
586
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Number of walks on a graph passing through a specific vertex
Let $\mathcal{G}$ be a simple (no self-edges) undirected graph with $N$ vertices, and denote $\mathbf{A}$ its adjacency matrix: $A_{ij}=1$ if there exists an edge between vertex $i$ and vertex $j$.
$ …
- 274
5
votes
0
answers
107
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Discrete random walk in an expanding cage (i.e. in a growing domain)
In the book "A guide to First-Passage Processes" by Sidney Redner, a section is dedicated to the survival probability of a random walker in a growing domain.
For a fixed-length interval $[0,L]$, the p …
- 274
4
votes
1
answer
444
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Derive the solution of the diffusion equation from the solution of a random walk
Summary
The probability distribution (pdf) of a random walk in 1 dimension is represented by a Bessel function. On the other hand, the pdf of a Brownian motion in free space is represented by a Gaussi …
- 274