Related papers: A Consistent Sandpile Torsor Algorithm for Regular…
We construct families of rational functions $f \colon \bP^1_k \to \bP^1_k$ of degree $d \geq 2$ over a perfect field $k$ whose associated fixed-point processes fail to be martingales. Conversely, for any normal variety $X \subset…
The combinatorial theory of rotor-routers has connections with problems of statistical mechanics, graph theory, chaos theory, and computer science. A rotor-router network defines a deterministic walk on a digraph G in which a particle walks…
We prove several superrigidity results for isometric actions on metric spaces satisfying some convexity properties. First, we extend some recent theorems of N. Monod on uniform and certain non-uniform irreducible lattices in products of…
Over the last thirty years, numerous consistency conditions for replicated data have been proposed and implemented. Popular examples of such conditions include linearizability (or atomicity), sequential consistency, causal consistency, and…
We study a class of dynamically consistent risk measures that robustify a time-homogeneous Markovian reference model by allowing for distributional uncertainty in its transition laws. We start from one-step convex risk evaluations in which…
Starting from the definition of a stiffness matrix, the authors present a new formulation of the Cartesian stiffness matrix of parallel mechanisms. The proposed formulation is more general than any other stiffness matrix found in the…
In this paper, we establish a regularity theory for the optimal transport problem when the target is composed of two disjoint convex domains. This is an important model in which singularities arise. Even though the singular set does not…
We provide a complete classification of when the homeomorphism group of a stable surface, $\Sigma$, has the automatic continuity property: Any homomorphism from Homeo$(\Sigma)$ to a separable group is necessarily continuous. This result…
The sandpile group of a connected graph is a group whose cardinality is the number of spanning trees. The group is known to have a canonical simply transitive action on spanning trees if the graph is embedded into the plane. However, no…
A separable, proper morphism of varieties with geometrically connected fibers induces a homotopy exact sequence relating the \'etale fundamental groups of source, target and fiber. Extending work of dos Santos, we prove the existence of an…
Kinetic self-avoiding trails are introduced and used to generate a substrate of randomly quenched flow vectors. Sandpile model is studied on such a substrate with asymmetric toppling matrices where the precise balance between the net…
Matsumoto proved in arXiv:1012.0981 that the prime end rotation numbers associated to an invariant annular continuum are contained in its rotation set. An alternative proof of this fact using only simple planar topology is presented.
Strongly regular graphs are regular graphs with a constant number of common neighbours between adjacent vertices, and a constant number of common neighbours between non-adjacent vertices. These graphs have been of great interest over the…
In this text we study the regularity of matrices with special polynomial entries. Barring some mild conditions we show that these matrices are regular if a natural limit size is not exceeded. The proof draws connections to generalized…
This paper is a sequel to [He7]. There a notion of marking of isolated hypersurface singularities was defined, and a moduli space $M_\mu^{mar}$ for marked singularities in one $\mu$-homotopy class of isolated hypersurface singularities was…
This paper proposes two novel nonlinear attitude filters evolved directly on the Special Orthogonal Group SO(3) able to ensure prescribed measures of transient and steady-state performance. The tracking performance of the normalized…
We consider the problem of decomposing the edges of a digraph into as few paths as possible. A natural lower bound for the number of paths in any path decomposition of a digraph $D$ is $\frac{1}{2}\sum_{v\in V(D)}|d^+(v)-d^-(v)|$; any…
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…
In this paper we treat faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties. By explicit calculation, we show that in each case, with essentially one exception (only in…
This paper integrates two strands of the literature on stability of general state Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric over Borel…