Papers by Hiroaki Yoshida
These are given as the cards on which some flow lines are drawn and increasing and decreasing of ... more These are given as the cards on which some flow lines are drawn and increasing and decreasing of the number of lines correspond to creation and annihilation, respectively. By the cards arrangement technique with these cards, of which machinery is the same as of the partition function for the lattice spins model in statistical mechanics, we write the moments of the $q$-Poisson random variable using the number of arc crossings, which is the same set partition statistic as restricted crossings investigated by P. Biane. This result suggests another $q$-deformed moments-cumulants relations, which interpolates between the usual and the free cases exactly. This is the joint work with Naoko Saitoh at Ochanomizu University.
Probability and Mathematical Statistics
Recently, Pfaffel and Schlemm have investigated the Mar-chenko-Pastur type limit (n → ∞ and limn→... more Recently, Pfaffel and Schlemm have investigated the Mar-chenko-Pastur type limit (n → ∞ and limn→∞n/p = λ > 0) of the sample covariance matrixp-1XntXn, where Xn is the p × n random matrix with dependence such that each row of Xn is given by a certain linear process. They have also determined the limit spectral measure by giving the functional equation for its Stieltjes transform. In this paper, we will see that such a limit spectral measure is a compound free Poisson law and, in the case where dependence is given by MA modeled Gaussian process, the sample covariance matrix can be regarded as compound Wishart matrix and, hence, gives the random matrix model for a compound free Poisson law. We will also give an application of compound Wishart matrix to the statistical data analysis of times series.
Quantum Probability, 2006
Journal of Chemical Software, 1999
Probability Theory and Related Fields, 1999
In usual probability theory, various characterizations of the Gaussian law have been obtained. Fo... more In usual probability theory, various characterizations of the Gaussian law have been obtained. For instance, independence of the sample mean and the sample variance of independently identically distributed random variables characterizes the Gaussian law and the property of remaining independent under rotations characterizes the Gaussian random variables. In this paper, we consider the free analogue of such a kind of characterizations replacing independence by freeness. We show that freeness of the certain pair of the linear form and the quadratic form in freely identically distributed noncommutative random variables, which covers the case for the sample mean and the sample variance, characterizes the semicircle law. Moreover we give the alternative proof for Nica's result that the property of remaining free under rotations characterizes a semicircular system. Our proof is more direct and straightforward one.
Studia Mathematica, 2013
Let , , and be the free additive, free multiplicative, and boolean additive convolutions, respect... more Let , , and be the free additive, free multiplicative, and boolean additive convolutions, respectively. For a probability measure µ on [0, ∞) with finite second moment, we find a scaling limit of (µ N) N as N goes to infinity. The R-transform of its limit distribution can be represented by Lambert's W-function. From this, we deduce that the limiting distribution is freely infinitely divisible, like the lognormal distribution in the classical case. We also show a similar limit theorem by replacing free additive convolution with boolean convolution.
A model for mathematics teacher knowledge based on the anthropological theory of didactics is pre... more A model for mathematics teacher knowledge based on the anthropological theory of didactics is presented together with a methodological discussion of how to assess such knowledge in practice. To this end we propose a concrete method involving "hypothetical teacher tasks" and individual as well as collaborative work of the teachers to be assessed. This discussion is illustrated by a small scale comparative study of how future lower secondary mathematics teachers (just about to graduate) from Denmark, France and Japan approach two hypothetical teacher tasks (related to teaching geometry and arithmetics). Résumé. Un modèle des connaissances de l'enseignant des mathématiques et une étude comparative du Danemark, de la France et du Japon. Nous présentons un modèle pour décrire les connaissances des enseignants des mathématiques, avec une discussion méthodologique de son application pour évaluer les connaissances en pratique. Nous proposons une méthode concrète impliquant un travail individuel et collectif des enseignants évalués sur des « tâches hypothétiques d'enseignant ». Cette discussion est illustrée par une étude à petite échelle, où nous comparons le travail de futurs enseignants de collège (à la fin leur formation) sur deux tâches hypothétiques d'enseignant relevant de l'enseignement de la géométrie et de l'arithmétique). Mots-clés. Connaissances professorales, comparaison internationale, similarité, Thalès, formation des enseignants, Danemark, France, Japon, théorie anthropologique du didactique And, upon the whole, a proof of a person's having knowledge is (…) the ability to teach; and for this reason we consider art, rather than experience, to be a science; for the artist can, wehereas the handicraftsmen cannot, convey instruction. (Aristotle, 1991, 13).
Entropy, 2012
Recently the identity of de Bruijn type between the relative entropy and the relative Fisher info... more Recently the identity of de Bruijn type between the relative entropy and the relative Fisher information with the reference moving has been unveiled by Verdú via MMSE in estimation theory. In this paper, we shall give another proof of this identity in more direct way that the derivative is calculated by applying integrations by part with the heat equation. We shall also derive an integral representation of the relative entropy, as one of the applications of which the logarithmic Sobolev inequality for centered Gaussian measures will be given.
Mathematische Zeitschrift, 1999
Discrete Mathematics, 2007
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Papers by Hiroaki Yoshida