Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Visit Stack Exchange
Stack Internal
Knowledge at work
Bring the best of human thought and AI automation together at your work.
Explore Stack InternalIt's somewhat counterintuitive that simple symmetric random walks in 1 dimension and in 2 dimensions return to the origin with probability 1.
Once one has absorbed that fact, it may be somewhat counterintuitive that the same thing is not true in higher dimensions.
(see Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$, Examples of results failing in higher dimensions, and Pólya's Random Walk ConstantPólya's Random Walk Constant)
It's somewhat counterintuitive that simple symmetric random walks in 1 dimension and in 2 dimensions return to the origin with probability 1.
Once one has absorbed that fact, it may be somewhat counterintuitive that the same thing is not true in higher dimensions.
(see Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$, Examples of results failing in higher dimensions, and Pólya's Random Walk Constant)
It's somewhat counterintuitive that simple symmetric random walks in 1 dimension and in 2 dimensions return to the origin with probability 1.
Once one has absorbed that fact, it may be somewhat counterintuitive that the same thing is not true in higher dimensions.
(see Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$, Examples of results failing in higher dimensions, and Pólya's Random Walk Constant)
It's somewhat counterintuitive that simple symmetric random walks in 1 dimension and in 2 dimensions return to the origin with probability 1.
Once one has absorbed that fact, it may be somewhat counterintuitive that the same thing is not true in higher dimensions.
(see Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$, Examples of results failing in higher dimensionsExamples of results failing in higher dimensions, and Pólya's Random Walk Constant)
It's somewhat counterintuitive that simple symmetric random walks in 1 dimension and in 2 dimensions return to the origin with probability 1.
Once one has absorbed that fact, it may be somewhat counterintuitive that the same thing is not true in higher dimensions.
(see Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$, Examples of results failing in higher dimensions, and Pólya's Random Walk Constant)
It's somewhat counterintuitive that simple symmetric random walks in 1 dimension and in 2 dimensions return to the origin with probability 1.
Once one has absorbed that fact, it may be somewhat counterintuitive that the same thing is not true in higher dimensions.
(see Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$, Examples of results failing in higher dimensions, and Pólya's Random Walk Constant)
It's somewhat counterintuitive that simple symmetric random walks in 1 dimension and in 2 dimensions return to the origin with probability 1.
Once one has absorbed that fact, it may be somewhat counterintuitive that the same thing is not true in higher dimensions.
(see Proving that $1$- and $2D$ simple symmetric random walks return to the origin with probability $1$, Examples of results failing in higher dimensions, and Pólya's Random Walk Constant)
