Search Results for "randomness"

The expected value B_n(s) of r^s from a fixed vertex of a unit n-cube to a point picked at random in the interior of the hypercube is given by B_n(s) = ...

A d-dimensional discrete percolation model is said to be inhomogeneous if different graph edges (in the case of bond percolation models) or vertices (in the case of site ...

In statistical mechanics, the two-dimensional Ising model is a popular tool used to study the dipole moments of magnetic spins. The Ising model in two dimensions is a type of ...

The expected number of real zeros E_n of a random polynomial of degree n if the coefficients are independent and distributed normally is given by E_n = ...

A sufficient condition on the Lindeberg-Feller central limit theorem. Given random variates X_1, X_2, ..., let <X_i>=0, the variance sigma_i^2 of X_i be finite, and variance ...

Given a unit line segment [0,1], pick two points at random on it. Call the first point x_1 and the second point x_2. Find the distribution of distances d between points. The ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

The problem of finding the strategy to guarantee reaching the boundary of a given region ("forest") in the shortest distance (i.e., a strategy having the best worst-case ...

The Lyapunov condition, sometimes known as Lyapunov's central limit theorem, states that if the (2+epsilon)th moment (with epsilon>0) exists for a statistical distribution of ...

Given a random variable x and a probability density function P(x), if there exists an h>0 such that M(t)=<e^(tx)> (1) for |t|<h, where <y> denotes the expectation value of y, ...