Modelling the economy

Why not model the economy as a Schramm–Loewner evolution where is drop in the dimension K corresponds to a drop in transaction rate, and therefore a drop in the degrees of motion.  They say:

the Schramm–Loewner evolution is conjectured or proved to describe the scaling limit of various stochastic processes in the plane...

This is nothing more than measure theory.  Mapping an aggregate process to a counting system.  It lists the various complexities of Brownian motion that describe a system with an given entropy dimension, or 'temperature'.  These motions which map into a planar distributions of 'quants'.  So it is back to the idea that the aggregate system is modelled as a finite grid system in which the finite grid is spread such that measurements uncertainty is relatively equal, in ratio, across the domain. Its the generalization of Shannon in that the SNR and exponents are matched, neither variable is given, the only given is the degree of Brownian motion allowed.

In economic terms this means we model the economy as unrestricted aggregate statistics, dimension eight, then degrade the performance by dropping the dimension K.  The maximum dimension is the sphere, which then degrades as the dimension degrades allowing only 'particle' motions within some limited angle smaller than Pi/2. On the tanh curve this means fewer solutions as dimension reduces, or it can be interpreted as a change in eccentricity. Hence we have a simple method to watch the sec stags progress as government debt grows, each loss of a dimension is a restriction on economic activity. The model is quantizing the law of diminishing returns.

Special values of κ

• κ = 2 corresponds to the loop-erased random walk, or equivalently, branches of the uniform spanning tree.
• For κ = 8/3 SLE_κ has the restriction property and is conjectured to be the scaling limit of self-avoiding random walks. A version of it is the outer boundary of Brownian motion. This case also arises in the scaling limit of critical percolation on the triangular lattice.
• κ = 3 is the limit of interfaces for the Ising model.
• For 0 ≤ κ ≤ 4 the curve γ(t) is simple (with probability 1).
• κ = 4 corresponds to the path of the harmonic explorer and contour lines of the Gaussian free field.
• For κ = 6 SLE_κ has the locality property. This arises in the scaling limit of critical percolation on the triangular lattice and conjecturally on other lattices.
• For 4 < κ < 8 the curve γ(t) intersects itself and every point is contained in a loop but the curve is not space-filling (with probability 1).
• κ = 8 corresponds to the path separating the uniform spanning tree from its dual tree.
• For κ ≥ 8 the curve γ(t) is space-filling (with probability 1).

The Markov property rules, there is no memory. All motions are aggregates of local values which add absolutely. Hence no trace of the history.  I think that means no redundant motion, hence maximizing entropy.