Slow Mixing of Glauber Dynamics for the Six-Vertex Model in the Ordered Phases

The six-vertex model in statistical physics is a weighted generalization of the ice model on Z^2 (i.e., Eulerian orientations) and the zero-temperature three-state Potts model (i.e., proper three-colorings). The phase diagram of the model represents its physical properties and suggests where local Markov chains will be efficient. In this paper, we analyze the mixing time of Glauber dynamics for the six-vertex model in the ordered phases. Specifically, we show that for all Boltzmann weights in the ferroelectric phase, there exist boundary conditions such that local Markov chains require exponential time to converge to equilibrium. This is the first rigorous result bounding the mixing time of Glauber dynamics in the ferroelectric phase. Our analysis demonstrates a fundamental connection between correlated random walks and the dynamics of intersecting lattice path models (or routings). We analyze the Glauber dynamics for the six-vertex model with free boundary conditions in the antiferroelectric phase and significantly extend the region for which local Markov chains are known to be slow mixing. This result relies on a Peierls argument and novel properties of weighted non-backtracking walks

Analyzing Boltzmann Samplers for Bose-Einstein Condensates with Dirichlet Generating Functions

Boltzmann sampling is commonly used to uniformly sample objects of a particular size from large combinatorial sets. For this technique to be effective, one needs to prove that (1) the sampling procedure is efficient and (2) objects of the desired size are generated with sufficiently high probability. We use this approach to give a provably efficient sampling algorithm for a class of weighted integer partitions related to Bose-Einstein condensation from statistical physics. Our sampling algorithm is a probabilistic interpretation of the ordinary generating function for these objects, derived from the symbolic method of analytic combinatorics. Using the Khintchine-Meinardus probabilistic method to bound the rejection rate of our Boltzmann sampler through singularity analysis of Dirichlet generating functions, we offer an alternative approach to analyze Boltzmann samplers for objects with multiplicative structure.Comment: 20 pages, 1 figur

Analysis of Markov chains and algorithms for ad-hoc networks

Issued as final reportNational Science Foundation (U.S.

The Other Side of the Moon: The Data Problem in Analyzing Growth Determinants

Replication of two recent studies of growth determinants shows that results are sensitive to the choice of data from which growth rates are calculated, especially with respect to whether economic convergence has occurred. Previous warnings against using data that has been adjusted to increase cross-country comparability to study within-country patterns over time (growth rates) have been largely ignored at the cost of possibly contaminating the conclusions.http://deepblue.lib.umich.edu/bitstream/2027.42/40068/3/wp682.pd

A Rise By Any Other Name? Sensitivity of Growth Regressions to Data Source

Measured rates of growth in real per capita income differ drastically depending on the data source. This phenomenon occurs largely because data sets differ in whether and how they adjust for changes in relative prices across countries. Replication of several recent studies of growth determinants shows that results are sensitive in important ways to the choice of data. Previous warnings against using data adjusted to increase cross-country comparability to study within-country patterns over time (growth rates) have been largely ignored at the cost of possibly contaminating the conclusions.http://deepblue.lib.umich.edu/bitstream/2027.42/64394/1/wp889.pd

A Rise by Any Other Name? Sensitivity of Growth Regressions to Data Source

Measured rates of growth in real per capita income differ drastically depending on the data source. This phenomenon occurs largely because data sets differ in whether and how they adjust for changes in relative prices across countries. Replication of several recent studies of growth determinants shows that results are sensitive in important ways to the choice of data. Previous warnings against using data adjusted to increase cross-country comparability to study within-country patterns over time (growth rates) have been largely ignored at the cost of possibly contaminating the conclusions.growth, measurement

A Rise By Any Other Name? Sensitivity of Growth Regressions to Data Source

Measured rates of growth in real per capita income differ drastically depending on the data source. This phenomenon occurs largely because data sets differ in whether and how they adjust for changes in relative prices across countries. Replication of several recent studies of growth determinants shows that results are sensitive in important ways to the choice of data. Previous warnings against using data adjusted to increase cross-country comparability to study within-country patterns over time (growth rates) have been largely ignored at the cost of possibly contaminating the conclusions.Growth, Measurement