On multiple Schramm–Loewner evolutions

On Multiple Schramm-Loewner Evolutions

In this note we consider the ansatz for Multiple Schramm-Loewner Evolutions (SLEs) proposed by Bauer, Bernard and Kytölä from a more probabilistic point of view. Here we show their ansatz is a consequence of conformal invariance, reparameterisation invariance and a notion of absolute continuity. In so doing we demonstrate that it is only consistent to grow multiple SLEs if their κ parameters ar...

Foundations of multiple black hole evolutions

Recent Evolutions of Multiple Sequence Alignment Algorithms

An ever-increasing number of biological modeling methods depend on the assembly of an accurate multiple sequence alignment (MSA). These include phylogenetic trees, profiles, and structure prediction. Assembling a suitable MSA is not, however, a trivial task, and none of the existing methods have yet managed to deliver biologically perfect MSAs. Many of the algorithms published these last years ...

Harmonic evolutions on graphs

We define the harmonic evolution of states of a graph by iterative application of the harmonic operator (Laplacian over Z2). This provides graphs with a new geometric context and leads to a new tool to analyze them. The digraphs of evolutions are analyzed and classified. This construction can also be viewed as a certain topological generalization of cellular automata. MSC: 05C50, 15A33, 05C75, ...

Multiple Schramm-Loewner Evolutions and Statistical Mechanics Martingales

A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to satisfy this condition leads to some natural processes, which we study in this note. We give examples of such multiple SLEs and discuss how a choice of conform...