01653nas 2200409 n 450 99000888393040332120240229084333.00065-0900000888393FED01000888393(Aleph)000888393FED01000888393CNRP 0009020720161109a19629999km-y0itaa50------bamulITauu--------Acta ad archaeologiam et artium historiam pertinentia1962-RomaGiorgio Bretscneider0010008883942001Acta ad archaeologiam et artium historiam pertinentia. Series altera in 8Acta ad archaeologiam et artium historiam pertinentia937902930INSTITUTUM ROMANUM NORVEGIAEITACNP20090723http://acnp.cib.unibo.it/cgi-ser/start/it/cnr/dc-p1.tcl?catno=59844&person=false&language=ITALIANO&libr=&libr_th=unina1Biblioteche che possiedono il periodicoSE990008883930403321BRAU. Biblioteca di Ricerca di Area Umanistica1962-Italia 409FLFBCFLFBCActa ad archaeologiam et artium historiam pertinentia802271UNINA866-01NA072 BRAU. Biblioteca di Ricerca di Area UmanisticaItalia 409Piazza Bellini 56/60, 80133 Napoli (NA)(081) 2533948itacnp.cib.unibo.itACNP Italian Union Catalogue of Serialshttp://acnp.cib.unibo.it/cgi-ser/start/it/cnr/df-p.tcl?catno=59844&language=ITALIANO&libr=&person=&B=1&libr_th=unina&proposto=NO04862nam 22007455 450 991068646820332120260408161613.0981-19-9527-310.1007/978-981-19-9527-9(CKB)5840000000241981(MiAaPQ)EBC7236610(Au-PeEL)EBL7236610(DE-He213)978-981-19-9527-9(OCoLC)1375994938(PPN)269657479(MiAaPQ)EBC7235390(EXLCZ)99584000000024198120230406d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierElliptic Extensions in Statistical and Stochastic Systems /by Makoto Katori1st ed. 2023.Singapore :Springer Nature Singapore :Imprint: Springer,2023.1 online resource (134 pages)SpringerBriefs in Mathematical Physics,2197-1765 ;47981-19-9526-5 Includes bibliographical references and index.Introduction -- Brownian Motion and Theta Functions -- Biorthogonal Systems of Theta Functions and Macdonald Denominators -- KMLGV Determinants and Noncolliding Brownian Bridges -- Determinantal Point Processes Associated with Biorthogonal Systems -- Doubly Periodic Determinantal Point Processes -- Future Problems.Hermite's theorem makes it known that there are three levels of mathematical frames in which a simple addition formula is valid. They are rational, q-analogue, and elliptic-analogue. Based on the addition formula and associated mathematical structures, productive studies have been carried out in the process of q-extension of the rational (classical) formulas in enumerative combinatorics, theory of special functions, representation theory, study of integrable systems, and so on. Originating from the paper by Date, Jimbo, Kuniba, Miwa, and Okado on the exactly solvable statistical mechanics models using the theta function identities (1987), the formulas obtained at the q-level are now extended to the elliptic level in many research fields in mathematics and theoretical physics. In the present monograph, the recent progress of the elliptic extensions in the study of statistical and stochastic models in equilibrium and nonequilibrium statistical mechanics and probability theory is shown. At the elliptic level, many special functions are used, including Jacobi's theta functions, Weierstrass elliptic functions, Jacobi's elliptic functions, and others. This monograph is not intended to be a handbook of mathematical formulas of these elliptic functions, however. Thus, use is made only of the theta function of a complex-valued argument and a real-valued nome, which is a simplified version of the four kinds of Jacobi's theta functions. Then, the seven systems of orthogonal theta functions, written using a polynomial of the argument multiplied by a single theta function, or pairs of such functions, can be defined. They were introduced by Rosengren and Schlosser (2006), in association with the seven irreducible reduced affine root systems. Using Rosengren and Schlosser's theta functions, non-colliding Brownian bridges on a one-dimensional torus and an interval are discussed, along with determinantal point processes on a two-dimensional torus. Their scaling limitsare argued, and the infinite particle systems are derived. Such limit transitions will be regarded as the mathematical realizations of the thermodynamic or hydrodynamic limits that are central subjects of statistical mechanics.SpringerBriefs in Mathematical Physics,2197-1765 ;47Mathematical physicsStochastic processesStatistical physicsQuantum theoryMathematical PhysicsStochastic ProcessesStatistical PhysicsQuantum PhysicsFuncions el·líptiquesthubProcessos estocàsticsthubFísica estadísticathubLlibres electrònicsthubMathematical physics.Stochastic processes.Statistical physics.Quantum theory.Mathematical Physics.Stochastic Processes.Statistical Physics.Quantum Physics.Funcions el·líptiquesProcessos estocàsticsFísica estadística515.983Katori Makoto1931-755845MiAaPQMiAaPQMiAaPQBOOK9910686468203321Elliptic Extensions in Statistical and Stochastic Systems3149417UNINA