Schramm–Loewner evolution

Hero mathematician of the day, Oded Schramm.

In 1999 he moved to the Theory Group at Microsoft Research in Redmond, Washington, where he remained for the rest of his life.

Microsoft stole this guy! He dies in a climbing accident in 2008 and we will miss some great triumphs in theory. This guy cracked the code in the new math, the math of minimally redundant systems. But the lesson is, mathematicians are worth more than their weight in gold, find them, hire them.

I will be talking about his work and how it relates.

He had two partners;

Wendelin Werner (born 23 September 1968) is a German-born French mathematician working in the area of self-avoiding random walks, Schramm-Loewner evolution, and related theories in probability theory and mathematical physics.

and  Gregory Francis Lawler (born July 14, 1955) is an American mathematician working in probability theory and best known for his work since 2000 on the Schramm–Loewner evolution.

The work is important in that it identifies the property of a lattice that defines finite elements conformal to calculus and conserves system properties. Redundancy, is my conjecture, that finite elements which are not martingale, that is retaining a memory of the past requires redundant motion.

I deal with congested systems, optimally congested. Motion is to achieve separation  but the congestion gradient is established by local interaction. As separation increases the separation gradient becomes uncertain, and there is no non-redundant exchange at some point.  That point is the point of optimum congestion. At this equilibrium, elements will operate with their congestion gradients intersecting at some uncertain center which should be minimum phase, or normally distributed . The elements reach a stopping point where movements perpendicular to the local radius are indistinguishable to movements along the radius. The elements are at maximum entropy and the uncertainty is fixed to the Fine Structure constant; and the curvature of the enclosing sphere estimates a rational Pi with optimum error. The system is spherically adiabatic.

The gradient changes as 1/r, r measured from a probable center. Hence the system must quantize motion along r and angle to maintain the martingale condition everywhere. Hence the unit almost sphere, otherwise known as particles.

What is t?

Well the only requirement is that it be a variable globally known and is not x. Most likely is is the unit of uncertainty, a quantization of  the Fine Structure  for the system. It is quantized for minimum redundancy which sub-selects solutions for x. p(t,x) still generates the martingales, within the limits of uncertainty. It is globally known because the minimal unit of the system has it built in.