Questions tagged [random-walks]

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15
votes
1answer
383 views

On “The Average Height of Planted Plane Trees” by Knuth, de Bruijn and Rice (1972)

I am trying to derive the classic paper in the title only by elementary means (no generating functions, no complex analysis, no Fourier analysis) although with much less precision. In short, I "only" ...
8
votes
2answers
2k views

Algorithm to generate self-avoiding random walk on a lattice

Where can I find some code to generate random self-avoiding walks on 2 and 3-dimensional lattices whose side-lengths are powers of two? The walk should pass through every point on the lattice More ...
6
votes
1answer
304 views

Generating uniform random connected graphs: doubt about Wilson's algorithm

I want to generate a random connected simple labeled graph with $n$ vertices and $m$ edges, selected uniformly over all connected graphs with such $n$ and $m$. I found this approach. It says: build a ...
4
votes
1answer
303 views

Examples for directed graphs with super polynomial cover time

The cover time of a graph is the expected number of steps in a random walk on the graph until we visit all the nodes. For undirected graphs the cover time is upperbounded by $O(n^3)$. What about ...
4
votes
1answer
120 views

Average vs Worst-Case Hitting Time

Consider a simple random walk on an undirected graph and let $H_{ij}$ be the hitting time from $i$ to $j$. How much bigger can $$ H_{\rm max} = \max_{i,j} H_{ij}, $$ be compared to $$ H_{\rm ave} = \...
3
votes
1answer
317 views

Quantum algorithms and quantum computation

Is my (very high-level) understanding correct here regarding quantum algorithms — Quantum computers can process a massive amount of operations in parallel to the nature of qubits and their ...
3
votes
1answer
171 views

Random Walk on the Integer Line

Suppose we are doing a random walk on the infinite integer line and that we take $2n$ total steps. At every step of this walk, the position of the walker is an integer point on this line. For the next ...
3
votes
1answer
405 views

How many random walks to start from each node?

Assume that we are given a real life graph, DBLP network in my case, where degree distribution of nodes follows a power law (many nodes have 1, 2 neighbors, and only a few nodes have hundreds of ...
3
votes
1answer
779 views

Generating a random path in a grid without deadlock

I want to write an algorithm that takes an $n \times n$ grid and a number $L$, generate a random walk of length $L$ on the grid that doesn't visit the same cell twice. One simple solution would be ...
2
votes
1answer
169 views

Increasing entropy of random walk

Let $P$ be a transition matrix of a random walk in an undirected (may not regular) graph $G$. Let $\pi$ be a distribution on $V(G)$. The Shannon entropy of $\pi$ is defined by $$H(\pi)=-\sum_{v \in ...
2
votes
1answer
75 views

Generate random matrix and its inverse

I want to randomly generate a pair of invertible matrices $A,B$ that are inverses of each other. In other words, I want to sample uniformly at random from the set of pairs $A,B$ of matrices such that ...
2
votes
1answer
43 views

Sampling in large graph using simple random walk

I'm studying sampling techniques in online social networks. The assumption is we don't have full access to the network(i.e, we don’t know the size of the network). However crawling is supported, i.e, ...
2
votes
1answer
109 views

Electrical resistance of expander graphs

Let $G$ be a $d$-regular expander graph. What is the electrical resistance of $G$? Is it a constant independent of the number of nodes $n$ once $d$ is large enough? If not, can we give matching upper ...
2
votes
1answer
108 views

2D random walk. Should both dimensions be independent?

My assignment is to compare several probability distributions in random walk algorithm. I'd like to analyse it in 2D linear space to make the concept more intuitive. What is the correct approach in ...
2
votes
0answers
120 views

Graph conductance - program/code/library

Technical question: is there any open source program/code/library which can compute (minimal) conductance of a given graph, probably by some simulated annealing? Think it is quite well-known problem, ...
1
vote
2answers
140 views

Random walk increasing distance

I'm wondering why if I increase the number of step in a set of simulation of a random walk on a grid the distance from the origin is higher. If I can move on the grid in 4 directions, there are 0.5 ...
1
vote
2answers
110 views

Random walks on Complete Binary Trees

Let $T$ be a complete binary tree of height $n$ and root $r$. A random walk starts at $r$, and at each step uniformly at random moves on a neighbor. There are $m$ random walkers all starting at $r$ ...
1
vote
1answer
42 views

Randomized algorithm for 2kCNF satisfiability problem

The problem: Let a formula in $\varphi\in 2kCNF$ where there's an assignment $\alpha$ such that for every clause, $l$ in $\varphi$, $\alpha$ satisfies at least $k$ literals of $l$. Suggest a ...
1
vote
0answers
49 views

MATLAB script to model biological branching process

I took an introductory MATLAB course a couple of years ago (and since then have only taken a basic C++ course) and am presently stumped as to how to start with a project I am undertaking. As part of ...
1
vote
0answers
102 views

Probability of finding the maximum element in a heap

You are given a minimum heap, with probability going to left is 50% and going to right is 50%. What is the probability that You will land up on a maximum element in the heap? For this scenario since ...
1
vote
0answers
22 views

Prior papers on hash walks [closed]

Random walks are well known from probability theory. I have the idea for hash walks. If h(x) is a hash function and a,b,c,d,e,f is a boolean sequence then the sort of hash walk I am talking about is ...
0
votes
1answer
265 views

Proving that the cover time for graph is exponential in the worst case

How can I prove that the cover time for a directed graph $G$ can be exponential in the size of $G$? The cover time is the expected length of a random walk that visits all vertices.
0
votes
0answers
40 views

$O(1)$ time, $O(1)$ state random access Brownian motion?

I would like to generate discrete samples $0 = B(0), B(1), \ldots, B(T)$ of a Brownian motion $B : [0,T] \to \mathbb{R}^d$. It is possible to get $O(\log T)$ time random access into a consistent ...
-1
votes
1answer
94 views

proof of convergence in arbitrary precision PRNGs

consider a program that generates a random walk using a PRNG, as in following pseudocode. it uses arbitrary precision arithmetic such that there is no limit on variable values (ie no overflow). ...