Laurence S. Field

Research

My interests lie in probability, conformal invariance and statistical physics. I have been working on aspects of the Schramm–Loewner evolution (SLE). Important tools are Brownian motion and related measures on planar curves.

Publications and Preprints

L. S. Field,   Two-sided radial SLE and length-biased chordal SLE.
Preprint, 29 pages.   arXiv:1601.03374

L. S. Field and G. F. Lawler,   Escape probability and transience for SLE.
Electronic Journal of Probability 20 (2015), no. 10, 1–14.   arXiv:1407.3314

L. S. Field and G. F. Lawler,   Reversed radial SLE and the Brownian loop measure.
Journal of Statistical Physics 150 (2013), no. 6, 1030–1062.   arXiv:1207.6360

Expository Work

An estimate for Brownian excursion measure.
This short note gives an elementary proof of a lemma from “Escape probability and transience for SLE”, above.

Parafermionic observables in discrete models and Schramm–Loewner evolution,
Topic proposal, February 2011.
 

Representations of GL(2) over finite and local fields,
Honours essay, October 2008.

Recent Talks

20 Jun 16   Stochastics Seminar, Aalto University

15 Jun 16   Recent developments in SLE, Inst. Mittag-Leffler

  9 Dec 15   ANZAMP Annual Meeting, Newcastle

28 Oct 15   Seminar on Stochastic Processes, ETH Zürich

23 Apr 15   Probability Seminar, Michigan State University

14 Mar 15   AMS Sectional Meeting, East Lansing

28 Aug 14   Weizmann Institute of Science, Rehovot
Geometric Functional Analysis and Probability Seminar

27 Aug 14   The Technion, Haifa
Probability and Stochastic Processes Seminar

  1 Aug 14   Sydney Dynamics Group
  Conformally invariant processes and SLE

Teaching

EPFL, Autumns 2015 and 2016: Lattice Models (master's course)

2014–15: Multivariable Calculus—Autumn (Math 195), Winter (Math 195).

I was the primary author of a new Linear Algebra text for Math 163 (March–June 2014):

• Vector Spaces and Linear Maps
• Matrices and Gaussian Elimination
• Eigenvalues and Determinants

2013–14: Honors Calculus (Math 161–162–163, Inquiry-Based Learning).

2012–13: Calculus—Autumn (Math 151), Winter (Math 152), Spring (Math 153).

2011–12: Calculus—Autumn (Math 151), Winter (Math 152), Spring (Math 153).

2010–11: Analysis in Rⁿ (Math 203–204–205, Inquiry-Based Learning).

Contact Details

laurence dot field at anu dot edu dot au

New web site at ANU

Dr Laurence Field
Research School of Finance, Actuarial Studies & Statistics
The Australian National University
26C Kingsley St
Acton, ACT, 2601
Australia

Simulations

WalkBoundary is a program to simulate large random walk loops and their boundaries. This is the same program as you see embedded above, but the downloadable version is capable of generating much larger loops. WalkBoundary is available for Mac or Windows, or as source code.

Three new simulations are available:

• Reverse Flow simulates chordal SLE using the reverse Loewner flow.
• Flow Line simulates chordal SLE_κ for κ<4 using Brent Werness’ new algorithm, based on Miller and Sheffield’s Imaginary Geometry.
• Percolation simulates the percolation exploration process.

All three are interactive animated simulations that you can control using the keyboard and mouse. (The colours have no meaning beyond tracking the time parametrization in the simulation.) There is an online version of each simulation (linked above), but the downloadable versions all run much faster, with a larger window on a longer path.
— Mac versions: Reverse Flow, Flow Line, Percolation. (For controls see “About box”.)
— Windows versions of all three simulations. (For controls see included text files.)
— Source code.

Important note on the Mac versions: All the Mac programs available here are unsigned. If the program refuses to run when you double-click it, then you need to right-click on the program's icon and select “Open”.