TAILIEUCHUNG - Đề tài " Isomonodromy transformations of linear systems of difference equations"

We introduce and study “isomonodromy” transformations of the matrix linear difference equation Y (z + 1) = A(z)Y (z) with polynomial A(z). Our main result is construction of an isomonodromy action of Zm(n+1)−1 on the space of coefficients A(z) (here m is the size of matrices and n is the degree of A(z)). The (birational) action of certain rank n subgroups can be described by difference analogs of the classical Schlesinger equations, and we prove that for generic initial conditions these difference Schlesinger equations have a unique solution. . | Annals of Mathematics Isomonodromy transformations of linear systems of difference equations By Alexei Borodin Annals of Mathematics 160 2004 1141 1182 Isomonodromy transformations of linear systems of difference equations By Alexei Borodin Abstract We introduce and study isomonodromy transformations of the matrix linear difference equation Y z 1 A z Y z with polynomial A z . Our main result is construction of an isomonodromy action of zm ra 1 -1 on the space of coefficients A z here m is the size of matrices and n is the degree of A z . The birational action of certain rank n subgroups can be described by difference analogs of the classical Schlesinger equations and we prove that for generic initial conditions these difference Schlesinger equations have a unique solution. We also show that both the classical Schlesinger equations and the Schlesinger transformations known in isomonodromy theory can be obtained as limits of our action in two different limit regimes. Similarly to the continuous case for m n 2 the difference Schlesinger equations and their ợ-analogs yield discrete Painleve equations examples include dPII dPIV dPv and Ợ-PVI. Introduction In recent years there has been considerable interest in analyzing a certain class of discrete probabilistic models which in appropriate limits converge to well-known models of random matrix theory. The sources of these models are quite diverse they include combinatorics representation theory percolation theory random growth processes tiling models and others. One quantity of interest in both discrete models and their random matrix limits is the gap probability - the probability of having no particles in a given set. It is known due to works of many people see JMMS Me TW P HI BD that in the continuous random matrix type setup these probabilities can be expressed through solution of an associated isomonodromy problem for a linear system of differential equations with rational coefficients. The goal of this paper is to .

• Thạc sĩ - Tiến sĩ - Cao học
• Isomonodromy transformations
• subjects of mathematics
• Annals of Mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• Research methods
• Data collection methods
• Understanding scientific research
• Ensuring research validity
• Measurement techniques
• Sampling methods
• Scientific research capacity
• Educational institutions
• Policy and management studies
• Vietnam Academy for Ethnic minorities
• Scientific bases
• earth sciences
• Research
• VNU Journal of Science
• scientific reports
• Action research
• linguistics
• research projects
• Foreign Languages
• cooperative research
• Renewable energy
• Introduction to research
• Scientific investigation
• Scientific investigation research
• Experimental designs
• Measurement of variables
• Reading research
• Conducting and reading research
• Research process
• Research report
• Purpose of research
• Scientific method
• Conducting research
• The effect of university autonomy on training and scientific research
• Vietnam national university of agriculture
• Training and scientific research
• Vascular plant
• Flora
• Yen Tu
• Quang Ninh Research Forest
• statements and documents scientific reports
• medical reports
• medical knowledge
• medical research
• clinical trials
• medical management
• health care
• Methods in behavioral research
• Behavioral research
• Scientific understanding
• Fundamental research issues
• Measurement concepts
• Observational methods
• reading comprehension
• education
• optimal picket
• model creation
• urban expansion
• organizing spatial
• Journal of Science
• Journal of Technology
• Technology Management
• Research quality
• Strategy and policy
• Summary of Doctoral thesis
• Summary of Doctoral thesis in public Management
• State management
• Female scientific research human
• Research human resource development
• Scientific research and teaching
• Defense and security education
• Current situation and solutions
• Security education
• Structural biochemistry
• epigenetics
• MicroRNAs
• Tạp chí khoa học
• Tạp chí Công nghệ
• Quản lý công nghệ
• Human resources
• Science management
• Poliomyelitis vaccine Research
• Non Ri Maprec
• Production center