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The Metropolis algorithm is a widely used procedure for sampling
from a specified distribution on a large finite set. We survey what is
rigorously known about running times. This includes work from ...
This paper develops bounds on the rate of decay of powers of Markov kernels
on finite state spaces. These are combined with eigenvalue estimates to give
good bounds on the rate of convergence to sta...
POSSIBLE INDICES FOR THE GALOIS IMAGE OF ELLIPTIC CURVES OVER
GALOIS IMAGE ELLIPTIC CURVES OVER
2015/8/26
POSSIBLE INDICES FOR THE GALOIS IMAGE OF ELLIPTIC CURVES OVER.
We prove many new cases of the Inverse Galois Problem for those simple groups arising fromorthogonal groups over finite fields. For example, we show that the finite simple groups Ω2n+1(p) and P&...
The L2-cutoff for reversible Markov processes
L2-cutoff Markov semigroups Normal operators
2015/8/26
We consider the problem of proving the existence of an L2-cutoff for families of ergodic Markov processes
started from given initial distributions and associated with reversible (more, generally, nor...
LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS
Sobolev inequality MARKOV CHAINS
2015/8/26
This is an expository paper on the use of logarithmic Sobolev inequalities
for bounding rates of convergence of Markov chains on finite state
spaces to their stationary distributions. Logarithmic So...
We introduce geometric comparison inequalities that give bounds on the eigenvalues of a reversible Markov chain in terms of the eigenvalues of a second chain. The bounds are applied to get sharp resul...
We present a simple and direct proof of the equivalence of various
functional inequalities such as Sobolev or Nash inequalities. This
proof applies in the context of Riemannian or sub-elliptic geome...
Equidistribution of Horocyclic Flows on Complete Hyperbolic Surfaces of Finite Area
Horocyclic Flows Complete Hyperbolic Surfaces Finite Area
2015/8/26
We provide a self-contained, accessible introduction to Ratner’s Equidistribution Theorem in the special case of horocyclic flow on a complete hyperbolic surface of finite area. This equidistribution ...
AN ANALYTIC CONSTRUCTION OF THE DELIGNE-MUMFORD COMPACTIFICATION OF THE MODULI SPACE OF CURVES
ANALYTIC CONSTRUCTION DELIGNE-MUMFORD COMPACTIFICATION MODULI SPACE OF CURVES
2015/8/26
In 1969, P. Deligne and D. Mumford compactified the modulispace of curves Mg,n. Their compactification Mg,n is a projective algebraic variety, and as such, it has an underlying analytic structure. Alt...
We are still far from a comprehensive theory of bifurcation in dynamical systems with
multiple time scales. However, systematic application of geometric methods and study
of examples have produced d...
We develop a general technique for proving the existence of chaotic attractors
for three-dimensional vector fields with two time scales. Our results connect
two important areas of dynamical systems:...
Folded nodes occur in generic slow-fast dynamical systems with two slow variables. Open regions
of initial conditions flow into a folded node in an open set of such systems, so folded nodes are an
i...
Lateral stability of the spring-mass hopper suggests a two-step control strategy for running
spring-mass hopper suggests control strategy
2015/8/25
This paper investigates the control of running gaits in the context of a spring loaded inverted
pendulum model in three dimensions. Specifically, it determines the minimal number of steps
required f...
THE BACKWARD BEHAVIOR OF THE RICCI AND CROSS CURVATURE FLOWS ON SL(2,R)
THE RICCI CROSS CURVATURE FLOWS
2015/8/25
This paper is concerned with properties of maximal solutions of the
Ricci and cross curvature flows on locally homogeneous three-manifolds of type
SL2(R). We prove that, generically, a maximal solut...