Erik Broman- Higher Dimensional Stick Percolation

Explore the mathematical foundations and applications of higher dimensional stick percolation in this 30-minute lecture by Erik Broman at the Hausdorff Center for Mathematics. Delve into the evolution of the stick percolation model from its introduction by R. Roy in 1991 to its current applications in physics and chemistry, including thin film transistors and nano-wire conductivity. Examine the extension of the model to arbitrary dimensions, focusing on sticks with specific lengths, widths, and orientations. Investigate the critical parameter for percolation and its scaling with stick length as it approaches infinity. Gain insights into the mathematical and application backgrounds, concrete examples, and the cylinder process. Learn about the stick model in Rd, intuition in two dimensions, and its extension to higher dimensions. Conclude with a sketch of the proof, including both lower and upper bounds.

Outline
Mathematical background
Applications background
A concrete application
Another mathematical motivation
The cylinder process
The stick model in Rd
The intuition in two dimensions
Higher dimensions
Sketch of proof (lower bound).
Sketch of proof.