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Hace 5 días · Random matrix theory (RMT) is the study of properties of random matrices, often as they become large. RMT provides techniques like mean-field theory , diagrammatic methods, the cavity method , or the replica method to compute quantities like traces , spectral densities , or scalar products between eigenvectors.
Hace 1 día · Cryptography, or cryptology (from Ancient Greek: κρυπτός, romanized : kryptós "hidden, secret"; and γράφειν graphein, "to write", or -λογία -logia, "study", respectively [1] ), is the practice and study of techniques for secure communication in the presence of adversarial behavior. [2]
Hace 2 días · In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time. In Albert Einstein 's 1905 treatment, the theory is presented as being based on just two postulates: [p 1] [1] [2] The laws of physics are invariant (identical) in all inertial frames of reference ...
Hace 4 días · t. e. In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. [1] [2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events ( subsets of the sample space).
Hace 3 días · Nicolas Bourbaki ( French: [nikɔla buʁbaki]) is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure (ENS). Founded in 1934–1935, the Bourbaki group originally intended to prepare a new textbook in analysis. Over time the project became much more ambitious, growing into a large ...
Hace 3 días · Pascal and Fermat set the groundwork for the investigations of probability theory and the corresponding rules of combinatorics in their discussions over a game of gambling. Pascal, with his wager , attempted to use the newly developing probability theory to argue for a life devoted to religion, on the grounds that even if the probability of success was small, the rewards were infinite.
Hace 3 días · Ergodicity. In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense. This implies that the average behavior of the system can be deduced from the trajectory of a "typical ...
