The perimeter of large planar Voronoi cells: a double-stranded random walk

Let $p\_n$ be the probability for a planar Poisson-Voronoi cell to have exactly $n$ sides. We construct the asymptotic expansion of $\log p\_n$ up to terms that vanish as $n\to\infty$. We show that {\it two independent biased random walks} executed by the polar angle determine the trajectory of the cell perimeter. We find the limit distribution of (i) the angle between two successive vertex vectors, and (ii) the one between two successive perimeter segments. We obtain the probability law for the perimeter's long wavelength deviations from circularity. We prove Lewis' law and show that it has coefficient 1/4.Comment: Slightly extended version; journal reference adde

Does the Death Penalty Still Matter: Reflections of a Death Row Lawyer

This talk was given by Professor David Bruck for the Frances Lewis Law Center at Washington and Lee University School of Law, April, 2002. It is a follow-up to “Does the Death Penalty Matter?,” given by Professor Bruck as the 1990 Ralph E. Shikes Lecture at Harvard Law School

Faith in the Republic: A Frances Lewis Law Center Conversation

None available

Faith in the Republic: A Frances Lewis Law Center Conversation

This is a spontaneous conversation discussing Hauserwas’ singular political theology in response to Levinson and Tushnet’s constitutional jurisprudence. It developed into a highly interesting debate concerning constitutional faith. This conversation was recorded at Washington and Lee’s Law Center on December 11, 1987

Faith in the Republic: A Frances Lewis Law Center Conversation

This is a spontaneous conversation discussing Hauserwas’ singular political theology in response to Levinson and Tushnet’s constitutional jurisprudence. It developed into a highly interesting debate concerning constitutional faith. This conversation was recorded at Washington and Lee’s Law Center on December 11, 1987

W&L Law Fall Scholarship Celebration 2019

On October 15, 2019, the Washington and Lee Law Library hosted the third bi-annual W&L Law Fall Scholarship Celebration. The event was co-sponsored by the Frances Lewis Law Center and took place in the Law Library\u27s main reading room from 4:30 to 6:30 p.m. On display were dozens of scholarly articles, books, and chapters authored by the W&L Law faculty and student body during 2018 and 2019, with hundreds of additional works accessible online through the Scholarly Commons institutional repository. Faculty, librarians, staff, and administrators mingled with law students over hors d\u27oeuvres and wine to peruse the formidable scholarly output of the W&L Law community. Spouses, alumni, faculty from W&L\u27s undergraduate campus, and others with ties to the University were also in attendance. Brant J. Hellwig, dean of W&L Law, and Christopher B. Seaman, director of the Frances Lewis Law Center, provided welcoming remarks introduced by W&L Law Library director Alex Zhang. The event program, which includes a list of the scholarship on display, is available to download in PDF. Photos taken at the event are also available to view in the W&L Law Scholarly Commons Image Gallery

Asymptotic statistics of the n-sided planar Poisson-Voronoi cell. I. Exact results

We achieve a detailed understanding of the $n$-sided planar Poisson-Voronoi cell in the limit of large $n$. Let ${p}\_n$ be the probability for a cell to have $n$ sides. We construct the asymptotic expansion of $\log {p}\_n$ up to terms that vanish as $n\to\infty$. We obtain the statistics of the lengths of the perimeter segments and of the angles between adjoining segments: to leading order as $n\to\infty$, and after appropriate scaling, these become independent random variables whose laws we determine; and to next order in $1/n$ they have nontrivial long range correlations whose expressions we provide. The $n$-sided cell tends towards a circle of radius (n/4\pi\lambda)^{\half}, where $\lambda$ is the cell density; hence Lewis' law for the average area $A\_n$ of the $n$-sided cell behaves as $A\_n \simeq cn/\lambda$ with $c=1/4$. For $n\to\infty$ the cell perimeter, expressed as a function $R(\phi)$ of the polar angle $\phi$, satisfies $d^2 R/d\phi^2 = F(\phi)$, where $F$ is known Gaussian noise; we deduce from it the probability law for the perimeter's long wavelength deviations from circularity. Many other quantities related to the asymptotic cell shape become accessible to calculation.Comment: 54 pages, 3 figure

Discretion in Making Legal Decisions: A Frances Lewis Law Center Colloquium

Colloquium papers, pp. 1161-1311, edited by Professor Shaffer