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KINETIC HIERARCHIES AND MACROSCOPIC LIMITS FOR CRYSTALLINE STEPS IN 1+1 DIMENSIONS
kinetic theory epitaxial growth crystal surface Burton–Cabrera–Frank model particle system Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy closure evaporation-condensation surface diffusion correlation function step chemical potential macroscopic limit propagation of chaos
2015/10/16
We apply methods of kinetic theory to study the passage from particle systems to nonlinear partial differential equations (PDEs) in the context of deterministic crystal surface relaxation. Starting wi...
SCALING LIMITS OF RECURRENT EXCITED RANDOM WALKS ON INTEGERS
Limit random walk RECURRENT EXCITED
2015/9/29
We describe scaling limits of recurrent excited random walks (ERWs) on
Z in i.i.d. cookie environments with a bounded number of cookies per site. We allow
both positive and negative excitations.
Given a sequence {αn} in (0, 1) converging to a rational, we examine
the model theoretic properties of structures obtained as limits of ShelahSpencer
graphs G(m, m−αn ). We show that in most c...
Henon Mappings in the Complex Domain II:projective and inductive limits of polynomials
Henon Mappings Complex Domain projective and inductive limits
2015/8/26
Henon Mappings in the Complex Domain II:projective and inductive limits of polynomials.
EXPONENTIAL THURSTON MAPS AND LIMITS OF QUADRATIC DIFFERENTIALS
Quadratic differential decomposition limit model iteration exponential map classification
2015/8/26
In the theory of iterated rational maps, the easiest maps to understand are postcritically finite: maps whose critical orbits are all periodic or preperiodic. These maps are also the most important ma...
Information Theoretic Limits on Learning Stochastic Differential Equations
Stochastic differential equation the coefficient
2015/8/21
Consider the problem of learning the drift coefficient of a stochastic differential equation from a sample path. In this paper, we assume that the drift is parametrized by a highdimensional vector. We...
Scaling Limits for Internal Aggregation Models with Multiple Sources
Scaling Limits Internal Aggregation Models Multiple Sources
2015/8/14
We study the scaling limits of three different aggregation models on Zd: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which parti...
Linear controller design: Limits of performance via convex optimization
Linear controller design convex optimization linear control system the convex optimization algorithm the controller the transfer matrix
2015/8/12
In this tutorial, an approach to the analysis and design of linear control systems based on numerical convex optimization over closed-loop maps is presented. Convexity makes numerical solution effecti...
Closed-loop convex analysis of performance limits for linear control systems
Linear control system computer aided control system and design a linear controller convex optimization digital signal processor
2015/8/12
In closed-loop convex analysis and design, the linear controller design problem is reformulated as a convex optimization problem, which may be more easily solved than the problems resulting from conve...
This paper reviews several mathematical techniques that have been developed to analyze the asymptotic behavior of waves and particles propagating in a heterogeneous medium. The heterogeneous medium is...
GRAPH LIMITS AND EXCHANGEABLE RANDOM GRAPHS
Figure restrictions and can exchange random graph
2015/7/8
GRAPH LIMITS AND EXCHANGEABLE RANDOM GRAPHS。
THRESHOLD GRAPH LIMITS AND RANDOM THRESHOLD GRAPHS
Limit theory the threshold figure model random threshold figure
2015/7/8
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.
INTERVAL GRAPH LIMITS
Figure limit theory the density range chart symmetric function uniform interval coordinate distribution
2015/7/7
We work out the graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W(x; y) on the unit square, with x and y ...
Visual limits of maximal flats in symmetric spaces and Euclidean buildings
visual limit geometric limit CAT(0) geometry geodesic boundary convex subset maximal flat symmetric space of non-compact type Euclidean building topological spherical building
2012/6/25
Let X be a symmetric space of non-compact type or a locally finite, strongly transitive Euclidean building, and let B denote the geodesic boundary of X. We reduce the study of visual limits of maximal...
A Smale space is a chaotic dynamical system with canonical coordinates of contracting and expanding directions. The basic sets for Smale's Axiom A systems are a key class of examples. We consider the ...