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      A stochastic process is a collection of random variables usually indexed by a totally ordered set.

      5
      votes
      0answers
      Let $\mathbb{Z}^d$ be the usual $d$-dimensional lattice and let $\mathbb{H}:=\mathbb{Z}^{d-1}\times Z_+$, where $Z_+:=[0,1,2,\ldots]$. If we now consider bond percolation on $\mathbb{H}$, it is a wel …
      asked Feb 7 '12 by Alex R.
      2
      votes
      0answers
      I've seen the following remark in a number of papers but don't know what to make of it. In this paper by Cohn, Elkies and Propp, it is mentioned that the normalized average Height function $\mathcal{H …
      asked Mar 26 '14 by Alex R.
      11
      votes
      1answer
      Consider a Markov chain on $\mathbb{Z}^d$ with transition kernel $P$ for adjacent vertices (non-diagonal). Essentially this is a $d$ dimensional random walk with the probability of a transition depend …
      asked Apr 23 '11 by Alex R.
      3
      votes
      1answer
      This question is somewhat related to this one. Loosely speaking, when should I expect a GOE/GUE distribution? The angle of my approach to this is not through statements such as "there is a natural inv …
      asked Mar 11 '14 by Alex R.
      11
      votes
      2answers
      While doing laundry at my local laundromat, I saw a coin pusher game. Below is a picture, and here is a video depicting how it works (disregard non-coins). alt text http://www.simpalife.com/wp-conte …
      asked Sep 13 '11 by Alex R.
      3
      votes
      1answer
      Let $\gamma(i)$ be a self avoiding walk (SAW) on a 2D lattice $L$ (a square lattice for example) starting at a predefined origin ( $\gamma(0)=(0,0)$ ) and having length $n:=\ell(\gamma)$. Furthermore, …
      asked Feb 2 '11 by Alex R.
      7
      votes
      2answers
      Take a simple random walk $\gamma$ in the complex plane conditioned to start at point $a$ and end at point $b$. For this random walk, we can define the winding number $W_\gamma(a,b)$ around $b$ in the …
      asked Oct 13 '10 by Alex R.
      5
      votes
      1answer
      Let $D$ be the set of all Dyck paths on square grid of size $n\times n$. For any particular Dyck path, let $S(t)=X_1+X_2+\ldots +X_t$ store the path, where $X_i=\pm 1$. Being a Dyck path, we have $S(0 …
      asked Apr 10 '13 by Alex R.
      10
      votes
      8answers
      Wigner's semicircle distribution is: $$f(x)=\frac{1}{2 \pi}\sqrt{4-x^2}, \ \ -2\leq x\leq 2.$$ Under reasonable conditions, the rescaled eigenvalue density of random symmetric matrices $M_n$ follows …
      asked Jun 19 '15 by Alex R.
      2
      votes
      0answers
      Let $M$ come from an ensemble of $N\times N$ matrices. The Wigner surmise is density function $p^W_0(s)=\frac{\pi}{2}se^{-\pi s^2/4}$. From a random matrix point of view, we can write $\rho^W_0(s)=\fr …
      asked Oct 3 '14 by Alex R.
      3
      votes
      1answer
      In this paper by Nordenstam, it is shown that a certain interlacing particle process that arises from uniformly random Aztec diamond tilings is amazingly similar to Warren's process. One of the result …
      asked Jan 27 '14 by Alex R.

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