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Results tagged with pr.probability
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user 420641
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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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
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2
answers
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Evolution of the empirical mean of a list as we remove elements proportional to their value
Consider a list of $N$ integers $k_1,k_2,\dots k_N$, drawn independently from some distribution $P(k)$ with $k_i \geq 1$. We denote its mean with $\langle k\rangle=\sum_{k=1}kP(k)$. The first two mome …
- 274
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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