Related papers: Hasard et d\'eterminisme chez Laplace
Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…
Probabilities is the English translation of the book Probabilit\'es Tome 1 and Tome 2. The mathematic content is authored by Prof. Jean-Yves Ouvrard. The English version has been done by his eldest son Dr. Xavier Ouvrard. In this first…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
This is a brief survey of classical and recent results about the typical behavior of eigenvalues of large random matrices, written for mathematicians and others who study and use matrices but may not be accustomed to thinking about…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…
This announcement describes a probabilistic approach to cascades which, in addition to providing an entirely probabilistic proof of the Kahane-Peyri\`ere theorem for independent cascades, readily applies to general dependent cascades.…
We consider Bayesian variable selection in sparse high-dimensional regression, where the number of covariates $p$ may be large relative to the samples size $n$, but at most a moderate number $q$ of covariates are active. Specifically, we…
The probabilistic interpretation of Laplace transforms is used to help to describe the Laplace Transform $L(s)$ of improper random variables. In particular, busy periods in queueing models are examined. The value of $L(0)$ is explained in…
One of the presuppositions of science since the times of Galileo, Newton, Laplace, and Descartes has been the predictability of the world. This idea has strongly influenced scientific and technological models. However, in recent decades,…
We attempt to make superdeterminism more intuitive, notably by simulating a deterministic model system, a billiard game. In this system an initial 'bang' correlates all events, just as in the superdeterministic universe. We introduce the…
The book A Treatise on Probability was published by John Maynard Keynes in 1921. It contains a critical assessment of the foundations of probability and of the current statistical methodology. As a modern reader, we review here the aspects…
This work starts from definition of randomness, the results of algorithmic randomness are analyzed from the perspective of application. Then, the source and nature of randomness is explored, and the relationship between infinity and…
In non-relativistic as well as in special relativistic quantum theory, {\em mass} and {\em charge} are {\em pure numbers} appearing in various (quantum) operators and admit {\em any values}, {\it ie}, values for these quantities are to be…
This article contributes to the debate of the meaning of relationalism and background independence, which has remained of interest in theoretical physics from Newton versus Leibniz through to foundational issues for today's leading…
Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially…
The aim of this article is twofold. First, we shall review and analyse the Neo-Kantian justification for the application of probabilistic concepts in physics that was defended by Hans Reichenbach early in his career, notably in his…
This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case study of definitions of randomness in…
The simultaneous appearance in May 2003 of four books on the Riemann hypothesis (RH) provoked these reflections. We briefly discuss whether the RH should be added as a new axiom, or whether a proof of the RH might involve the notion of…
The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of…