We give a proof of the sublinear tracking property for sample paths of random walks on various groups acting on spaces with hyperbolic-like properties. As an application, we prove sublinear tracking in Teichmüller distance for random walks on mapping class groups, and on Cayley graphs of a large class of finitely generated groups.

It is known that linear conic systems are a special case of setvalued sublinear mappings. Hence the latter subsumes the former. In this note we observe that linear conic systems also contain set-valued sublinear mappings as a special case. Consequently, the former also subsumes the latter.

In this short note we show that the outer norm of a sublinear mapping F, acting between Banach spaces X and Y and with domF = X, is finite only if F is single-valued. This implies in particular that for a sublinear multivalued mapping the inner and the outer norms cannot be finite simultaneously. AMS 2000 Subject Classification: 49J53, 47H04, 54C60.

A recent work (Wang et. al., NIPS 2015) gives the fastest known algorithms for orthogonal tensor decomposition with provable guarantees. Their algorithm is based on computing sketches of the input tensor, which requires reading the entire input. We show in a number of cases one can achieve the same theoretical guarantees in sublinear time, i.e., even without reading most of the input tensor. In...

We introduce the problem of augmenting graphs with sublinear memory in order to speed up replies to queries. As a concrete example, we focus on the following problem: the input is an (unpartitioned) bipartite graph G = (V,E). Given a query v ∈ V , the algorithm’s goal is to output v’s color in some legal 2-coloring of G, using few probes to the graph. All replies have to be consistent with the ...

From 17.07.05 to 22.07.05, the Dagstuhl Seminar 05291 Sublinear Algorithms was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are...

We show that Farkas’ lemma for linear inequality systems, established in 1902, continues to hold for separable sublinear inequality systems. As a consequence, we establish a qualification-free characterization of optimality for separable sublinear programming problems which include classes of robust linear programming problems.

We study functions whose directional derivatives can be written as a difference of two extended real valued sublinear function (ds functions). The pair of convex sets obtained as the support functions of these sublinear functions is provided by a familiar equivalence relation and is considered as the bisubdifferential of the function. We study calculus rules and give application to minimization...

A range of first-passage percolation type models are believed to demonstrate the related properties of sublinear variance and superdiffusivity. We show that directed last-passage percolation with Gaussian vertex weights has a sublinear variance property. We also consider other vertex weight distributions. Corresponding results are obtained for the ground state of the ‘directed polymers in a ran...