相关论文: On the correlation of the Moebius function with ra…

Using 1-loop renormalisation group equations, we analyze the effect of randomness on multi-critical unitary minimal conformal models. We study the case of two randomly coupled $M_p$ models and found that they flow in two decoupled $M_{p-1}$…

We study how maximal regularity estimates with respect to the continuous functions improve automatically in cases where the spatial norm is fundamentally different from the supremum norm. More precisely, we invoke properties such as weak…

We consider a class of non-homogeneous Markov chains, that contains many natural examples. Next, using martingale methods, we establish some deviation and moment inequalities for separately Lipschitz functions of such a chain, under moment…

Random partition models are widely used in Bayesian methods for various clustering tasks, such as mixture models, topic models, and community detection problems. While the number of clusters induced by random partition models has been…

A topological dynamical system induces two natural systems, one is on the hyperspace and the other one is on the probability space. The connection among some dynamical properties on the original space and on the induced spaces are…

In the framework of certain general probability theories of single systems, we identify various nonclassical features such as incompatibility, multiple pure-state decomposability, measurement disturbance, no-cloning and the impossibility of…

This paper extends classical probabilistic results to the broader class of demimartingales and demisubmartingales. We establish variants of Doob's-type optional sampling theorem under minimal structural conditions on stopping times, relying…

In this paper some sufficient conditions are given for when two bounded rank-one transformations are isomorphic or disjoint. For commensurate, canonically bounded rank-one transformations, isomorphism and disjointness are completely…

We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…

We deal with decay and boundedness properties of radial functions belonging to Besov and Lizorkin-Triebel spaces. In detail we investigate the surprising interplay of regularity and decay. Our tools are atomic decompositions in combination…

We prove that the M\"{o}bius function is linearly disjoint from an analytic skew product on the $2$-torus. These flows are distal and can be irregular in the sense that their ergodic averages need not exist for all points. The previous…

We study the convergence properties of a pair of learning algorithms (learning with and without memory). This leads us to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the…

We determine the M\"obius function of the poset of compositions of an integer. In fact we give two proofs of this formula, one using an involution and one involving discrete Morse theory. The composition poset turns out to be intimately…

We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation".…

Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…

We describe a Bayesian model for social learning of a random variable in which agents might observe each other over a directed network. The outcomes produced are compared to those from a model in which observations occur randomly over a…

We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…

The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…

First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…

We propose a relationship between the cohomology of arithmetic groups, and the motivic cohomology of certain (Langlands-)attached motives. The motivic cohomology group in question is that related, by Beilinson's conjecture, to the adjoint…