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We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…

Strongly consistent estimates are shown, via relative frequency, for the probability of "white balls" inside a dichotomous urn when such a probability is an arbitrary continuous time dependent function over a bounded time interval. The…

We use a tensor unfolding technique to prove a new identifiability result for discrete bipartite graphical models, which have a bipartite graph between an observed and a latent layer. This model family includes popular models such as…

In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties…

Several interesting models for contingency tables are defined by a system of equality and inequality constraints on a suitable set of marginal log-linear parameters. After reviewing the most common difficulties which are intrinsic to order…

Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…

Apportionment is the act of distributing the seats of a legislature among political parties (or states) in proportion to their vote shares (or populations). A famous impossibility by Balinski and Young (2001) shows that no apportionment…

We consider the development of adaptive, instance-dependent algorithms for interactive decision making (bandits, reinforcement learning, and beyond) that, rather than only performing well in the worst case, adapt to favorable properties of…

We consider settings where an allocation has to be chosen repeatedly, returns are unknown but can be learned, and decisions are subject to constraints. Our model covers two-sided and one-sided matching, even with complex constraints. We…

We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…

The asymptotic behaviour is studied of exponentially bounded sequences of codimensions of identities of algebras with unity. A series of algebras is constructed for which the base of the exponential increases by exactly one when an outer…

This paper is concerned with the convergence rate of policy iteration for (deterministic) optimal control problems in continuous time. To overcome the problem of ill-posedness due to lack of regularity, we consider a semi-discrete scheme by…

Clustering is a fundamental task in unsupervised learning. The focus of this paper is the Correlation Clustering functional which combines positive and negative affinities between the data points. The contribution of this paper is two fold:…

We model transport of individuals across a heterogeneous scale-free network where a few weakly connected nodes exhibit heavy-tailed residence times. Using the empirical law Axiom of Cumulative Inertia and fractional analysis we show that…

The reconstruction of interaction networks between random events is a critical problem arising from statistical physics and politics, sociology, biology, psychology, and beyond. The Ising model lays the foundation for this reconstruction…

This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…

A Gelfand-Tsetlin scheme of depth N is a triangular array with m integers at level m, m=1,...,N, subject to certain interlacing constraints. We study the ensemble of uniformly random Gelfand-Tsetlin schemes with arbitrary fixed N-th row. We…

Two main procedures characterize the way in which social actors evaluate the qualities of the options in decision-making processes: they either seek to evaluate their intrinsic qualities (individual learners), or they rely on the opinion of…

We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…

We study quasiperiodically forced circle endomorphisms, homotopic to the identity, and show that under suitable conditions these exhibit uncountably many minimal sets with a complicated structure, to which we refer to as `strangely…