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Pál Burai

Publications and source records attributed to Pál Burai.

6 recordsLinked to original sources
arXiv2024

Mathematical model of information bubbles on networks

The main goal of this paper to introduce a new model of evolvement of narratives (common opinions, information bubble) on networks. Our main tools come from invariant mean theory and graph theory. The case, when the root set of the network (influencers, news agencies, etc.) is ergodic is fully discussed. The other possibility, when the root contains more than one component is partially discussed and it could be a motivation for further research.

cs.SI↗
arXiv2022

A dichotomy result for strictly increasing bisymmetric maps

In this paper we show some remarkable consequences of the method which proves that every bisymmetric, symmetric, reflexive, strictly monotonic binary map on a proper interval is continuous, in particular it is a quasi-arithmetic mean. Now we demonstrate that this result can be refined in the way that the symmetry condition can be weakened by assuming symmetry only for a pair of distinct points of an interval.

math.CA↗
arXiv2021

Random means generated by random variables: expectation and limit theorems

We introduce the notion of a random mean generated by a random variable and give a construction of its expected value. We derive some sufficient conditions under which strong laws of large numbers and some limit theorems hold for random means generated by the elements of a sequence of independent and identically distributed random variables.

math.PR↗
arXiv2021

Characterization of quasi-arithmetic means without regularity condition

In this paper we show that bisymmetry, which is an algebraic property, has a regularity improving feature. More precisely, we prove that every bisymmetric, partially strictly monotonic, reflexive and symmetric function $F:I^2\to I$ is continuous. As a consequence, we obtain a finer characterization of quasi-arithmetic means than the classical results of Aczél, Kolmogoroff, Nagumo and de Finetti.

math.CA↗
arXiv2021

Limit theorems for Bajraktarević and Cauchy quotient means of independent identically distributed random variables

We derive strong laws of large numbers and central limit theorems for Bajraktarević, Gini and exponential- (also called Beta-type) and logarithmic Cauchy quotient means of independent identically distributed (i.i.d.) random variables. The exponential- and logarithmic Cauchy quotient means of a sequence of i.i.d. random variables behave asymptotically normal with the usual square root scaling just like the geometric means of the given random variables. Somewhat surprisingly, the multiplicative Cauchy quotient means of i.i.d. random variables behave asymptotically in a rather different way: in order to get a non-trivial normal limit distribution a time dependent centering is needed.

math.PR↗