# Tagged Questions

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### Random walk on d-dimensional torus

I am reading the following paper: http://arxiv.org/pdf/1602.03849v2.pdf I will explain the general setup below. Let $x\in X=\mathbb{T}^d$, where $\mathbb{T}^d$ is the d dimensional torus. Let $\rho$ ...
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### Multi-particle random walks

Define a multi-particle "breeding" random walk $\mathcal{W_p}$ in $d$ dimensions, for $p \in (0,1)$ as follows: The state of $\mathcal{W_p}$ at integer time $t\geq 0$ consists of the pair $(k, x)$ ...
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### Hierarchical (Recursive) Random Walk (also known as Hierarchical Hidden Markov Model)

Consider the following hierarchical (recursive) random walk model, which is also known as the hierarchical hidden Markov model in computer science (https://en.wikipedia.org/wiki/...
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### Expected number of forward jumps to reach a given quantile of a rv [closed]

I'm a noob in randomized algorithm and ran into a problem(definitely not home work. I'm doing a self study out of my interest with help of my friends. I'm pursuing research career in a machine ...
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### 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) (...
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### Unidirectional continuous path discrete time random walk

Is there any material available to study on unidirectional continuous path discrete time random walk on a line interval. To say "unidirectional continuous path discrete time random walk on a line ...
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### Mixing time of lazy random walk on the directed cycle $C_n$

Briefly: A hint (if this is easy), reference or derivation would be of great help. The question Let $C_n$ be the directed cycle with loops in each of its $n$ vertices, and consider the random walk ...
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### Resources to study self-avoiding walks

What would the best resources be for someone who wants to study self-avoiding walks from a mathematical standpoint? I'm talking about seminal/important papers, good textbooks perhaps, things of that ...
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### Does walk on $Z^d$ with steps $(\pm 1,\pm1,\ldots,\pm 1)$ return to origin?

If the steps are iid uniform as in the title, is the return probability known? Is it positive? Answers, comments, references welcome. Clearly each of these steps is not equivalent to $d$ steps of type ...
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### What is the influence of unreliable comparisons on the results of sorting

Considering sorting algorithms based solely on binary comparisons of the elements to be sorted(algorithms such as insertion sort, selection sort, quicksort, and so on), what problems do we face when ...
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### Bound that random walk stays within with constant probability?

For one-dimensional random walk, it is well-known that if the walk goes for $n$ steps, with constant probability it ends within $\pm\sqrt{n}$. What is the bound, in terms of $n$, such that if the ...
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### 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 $1$...
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### Position likelihood in a 2D graph [closed]

I am looking for general principles or specific answers to this generic example. Assume a 2d grid with no boundaries and a roving dot (ant/drunk guy/particle) that is initially located at some ...
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### Distribution of $\max_{n \ge 0} S_n$, random walk

Say we have a random walk that is a nearest neighbor random walk on the integers where at each step the probability of moving one step to the right is $p$ and the probability of moving one step to the ...
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### Recurrence of Poisson binomial distributed random walk

Let $X_n$ be the outcome of a Bernoulli trial where the probability of getting 1 is $p_n$ and the probability of getting 0 is $1-p_n$, and let $S_n = \sum_{i=1}^n \left(X_i - \textrm{E} X_i \right)$. ...
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### Discrete random walk with uniformly distributed transition p, set initially

I've been working on a discrete version of the "unreliable friend" distribution. It would seem that what I've come up with is equivalent to the following random walk: Choose $p$ from $U(0,1)$ Start ...