  In this paper we study a model of random knots obtained by fixing a space
curve in $n$-dimensional Euclidean space with $n>3$, and orthogonally
projecting the space curve on to random $3$ dimensional subspaces. By varying
the space curve we obtain different models of random parametrized knots, and we
will study how the expectation value of the curvature changes as a function of
the initial parametrized space curve. In the case when the initial data is a
pair of space curves, or more generally a pair of manifolds satisfying certain
conditions on their dimension, then we obtain models of random links for which
we will give methods to compute the second moment of the linking number. As an
application of our computations, we will study numerous models of random knots
and links, and how to recover these models by appropriately choosing the
initial space curves to be projected.
