scholarly journals The geometric Burge correspondence and the partition function of polymer replicas

2021 ◽  
Vol 27 (5) ◽  
Author(s):  
Elia Bisi ◽  
Neil O’Connell ◽  
Nikos Zygouras
Keyword(s):  
Partition Function ◽  
Random Environment ◽  
Young Diagram ◽  
Integral Identity ◽  
Fundamental Relation ◽  
Birational Maps ◽  
Volume Preserving

AbstractWe construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We establish its fundamental relation to the geometric Robinson-Schensted-Knuth correspondence and to the geometric Schützenberger involution. We also show a number of properties of the geometric Burge correspondence, specializing them to the case of symmetric input arrays. In particular, our construction shows that such a mapping is volume preserving in log-log variables. As an application, we consider a model of two polymer paths of given length constrained to have the same endpoint, known as polymer replica. We prove that the distribution of the polymer replica partition function in a log-gamma random environment is a Whittaker measure, and deduce the corresponding Whittaker integral identity. For a certain choice of the parameters, we notice a distributional identity between our model and the symmetric log-gamma polymer studied by O’Connell, Seppäläinen, and Zygouras (2014).

scholarly journals A $q$-Robinson-Schensted-Knuth Algorithm and a $q$-Polymer

10.37236/6739 ◽  
2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Yuchen Pei
Keyword(s):  
Partition Function ◽  
Young Diagram ◽  
Joint Distribution ◽  
Law Of Large Numbers ◽  
Fixed Time ◽  
Partition Functions ◽  
Polymer Model ◽  
Input Matrix ◽  
Strong Law ◽  
Large Numbers

In Matveev-Petrov (2017) a $q$-deformed Robinson-Schensted-Knuth algorithm ($q$RSK) was introduced.In this article we give reformulations of this algorithm in terms of the Noumi-Yamada description, growth diagrams and local moves. We show that the algorithm is symmetric, namely the output tableaux pairs are swapped in a sense of distribution when the input matrix is transposed. We also formulate a $q$-polymer model based on the $q$RSK, prove the corresponding Burke property, which we use to show a strong law of large numbers for the partition function given stationary boundary conditions and $q$-geometric weights.We use the $q$-local moves to define a generalisation of the $q$RSK taking a Young diagram-shape of array as the input. We write down the joint distribution of partition functions in the space-like direction of the $q$-polymer in $q$-geometric environment, formulate a $q$-version of the multilayer polynuclear growth model ($q$PNG) and write down the joint distribution of the $q$-polymer partition functions at a fixed time.

Structural studies of small amorphous volumes by electron diffraction

1990 ◽  
Vol 48 (4) ◽  
pp. 122-123
Author(s):  
Pierre Moine
Keyword(s):  
Electron Diffraction ◽  
Born Approximation ◽  
Structural Information ◽  
Fundamental Relation ◽  
X Rays ◽  
Structural Studies ◽  
Diffraction Experiment ◽  
Transmission Electron ◽  
Amorphous Structures ◽  
Diffraction Patterns

Qualitatively, amorphous structures can be easily revealed and differentiated from crystalline phases by their Transmission Electron Microscopy (TEM) images and their diffraction patterns (fig.1 and 2) but, for quantitative structural information, electron diffraction pattern intensity analyses are necessary. The parameters describing the structure of an amorphous specimen have been introduced in the context of scattering experiments which have been, so far, the most used techniques to obtain structural information in the form of statistical averages. When only small amorphous volumes (< 1/μm in size or thickness) are available, the much higher scattering of electrons (compared to neutrons or x rays) makes, despite its drawbacks, electron diffraction extremely valuable and often the only feasible technique.In a diffraction experiment, the intensity IN (Q) of a radiation, elastically scattered by N atoms of a sample, is measured and related to the atomic structure, using the fundamental relation (Born approximation) : IN(Q) = |FT[U(r)]|.

Driven periodic structures in random environment

1999 ◽  
Vol 09 (PR10) ◽  
pp. Pr10-85-Pr10-87
Author(s):  
V. M. Vinokur
Keyword(s):  
Random Environment ◽  
Periodic Structures

Driven elastic system in a random environment

1999 ◽  
Vol 09 (PR10) ◽  
pp. Pr10-69-Pr10-71 ◽  
Author(s):  
P. Chauve ◽  
T. Giamarchi ◽  
P. Le Doussal
Keyword(s):  
Random Environment ◽  
Elastic System

CALCULATION OF ISOTOPIC REDUCED PARTITION FUNCTION RATIO FOR AQUA COMPLEXES OF MAGNESIUM CATION

2017 ◽  
pp. 138-145
Author(s):  
A.V. BOCHKAREV ◽  
◽  
S.L. BELOPUKHOV ◽  
A.V. ZHEVNEROV ◽  
S.V. DEMIN ◽  
...  
Keyword(s):  
Partition Function ◽  
Aqua Complexes ◽  
Magnesium Cation

The relation between philosophy of creativity and education in the knowledge society

2020 ◽  
pp. 49-57
Author(s):  
Ernesta Molotokienė
Keyword(s):  
Social Space ◽  
Knowledge Society ◽  
Research Work ◽  
Knowledge Worker ◽  
Modern Society ◽  
Educational Goals ◽  
Fundamental Relation ◽  
Educational Organizations ◽  
Technological Environment ◽  
Changing Knowledge

The aim of the article is to reveal a fundamental relation between the philosophy of creativity and education in the knowledge society. Knowledge society as a special social space of modern society is formed in the middle of the 20th century with a new system of educational organizations, therefore training a knowledge worker who is able to be productive in a rapidly changing knowledge and technological environment is one of the main challenges of modern education. The contemporary philosophy of creativity has an important impact on education in knowledge society. The creative nature of learning determines the knowledge worker’s ability to achieve social, technical and technological innovations, while research work forms a dynamic competence and socio-economic performance. The article stresses that creativity remains one of the most important educational goals of knowledge society.

Sign in / Sign up

Export Citation Format

Share Document