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EXCURSIONS AND OCCUPATION TIMES OF CRITICAL EXCITED RANDOM WALKS
EXCURSIONS AND OCCUPATION TIMES EXCITED RANDOM WALKS
2015/9/29
We consider excited random walks (ERWs) on integers in i.i.d. environments with a bounded number of excitations per site. The emphasis is primarily on
the critical case for the transition between rec...
THE VISITS TO ZERO OF A RANDOM WALK DRIVEN BY AN IRRATIONAL ROTATION
RANDOM WALK DRIVEN IRRATIONAL ROTATION
2015/9/29
The method is to nd the asymptotic behavior of the ergodic sums of L1
functions for linear
ows on the in nite staircase surface.
Our methods also provide a new proof of J. Beck's central limit th...
The entropy of coupled map lattices with respect to the group
of space-time translations is considered. We use the notion of generalized
Lyapunov spectra ([11]) to prove the analogue of Ruelle inequ...
We prove that in the space of all C
r
(r 1) partially hyperbolic
di eomorphisms, there is a C
1 open and dense set of accessible diffeomorphisms.
Given square matrices B and B0 with a poset-indexed block structure (for which an ij block is zero unless i 1 j), when are there invertible matrices U and V with this required-zero-block structure suc...
PATH METHODS FOR STRONG SHIFT EQUIVALENCE OF POSITIVE MATRICES
PATH METHODS STRONG SHIFT EQUIVALENCE POSITIVE MATRICES
2015/9/29
In the early 1990’s, Kim and Roush developed path methods for establishing strong shift equivalence (SSE) of positive matrices over a dense subring U of R. This paper gives a detailed, unified and gen...
THE DIFFUSION COEFFICIENT FOR PIECEWISE EXPANDING MAPS OF THE INTERVAL WITH METASTABLE STATES
DIFFUSION COEFFICIENT WITH METASTABLE STATES
2015/9/29
Consider a piecewise smooth expanding map of the interval possessing several
invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs).
REGULARITY OF ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR PIECEWISE EXPANDING UNIMODAL MAPS
INVARIANT MEASURES UNIMODAL MAPS
2015/9/29
An important discovery of the 20th century mathematics is that many deterministic
systems exhibit stochastic behavior. The stochasticity is caused by exponential divergence of nearby trajectories. Th...
An outer billard map F is defined outside a closed convex curve Γ in the
following way. Let z be a point on the plane. Consider the supporting
line L(z) from z to Γ such that Γ lies on the rig...
Crooked planes were defined by Drumm to bound fundamental polyhedra in Minkowski space for Margulis spacetimes.
They were extended by Frances to closed polyhedral surfaces in the
conformal com...
AFFINE CUBIC SURFACES AND RELATIVE SL(2)-CHARACTER VARIETIES OF COMPACT SURFACES
AFFINE CUBIC SURFACES RELATIVE SL(2)-CHARACTER
2015/9/29
A natural family of affine cubic surfaces arises from
SL(2)-characters of the 4-holed sphere and the 1-holed torus. The
ideal locus is a tritangent plane which is generic in the sense that
the...
FINITE-SIDED DEFORMATION SPACES OF COMPLETE AFFINE 3-MANIFOLDS
3-MANIFOLDS DEFORMATION SPACES
2015/9/29
A Margulis spacetime is a complete affine 3-manifold
M with nonsolvable fundamental group. Associated to every Margulis spacetime is a noncompact complete hyperbolic surface S.
We show that eve...
Motivated by Felix Klein’s notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on
topological spaces locally model...
Stretching Three-Holed Spheres and the Margulis Invariant
Margulis Invariant Three-Holed Spheres
2015/9/29
This paper applies the authors’ forthcoming work, ”Affine deformations of a three-holed sphere” in Lorentzian geometry to prove a result in
hyperbolic geometry. Namely, an infinitesimal de...
ACTION OF THE JOHNSON-TORELLI GROUP ON REPRESENTATION VARIETIES
JOHNSON-TORELLI mapping class group
2015/9/29
Let Σ be a compact orientable surface with genus g and n boundary components B = (B1,...,Bn). Let c = (c1,...,cn) ∈ [−2,2]n. Then the
mapping class group MCG of Σ acts on the relative SU(2)-cha...