Integrable probability: From representation theory to Macdonald processes

Integrable probability: From representation theory to Macdonald processes

These are lecture notes for a mini-course given at the Cornell Probability Summer School in July 2013. Topics include lozenge tilings of polygons and their representation theoretic interpretation, the (q, t)-deformation of those leading to the Macdonald processes, nearest neighbor dynamics on Macdonald processes, their limit to semi-discrete Brownian polymers, and large time asymptotic analysis...

Changing the Role of Teacher according to Complexity Theory: From Representation to Facilitating Emergence

The present study seeks to rethink the role of the teacher in the teaching-learning process according to the complexity theory. First, the role of the teacher is explained in the traditional vision of Comenius and Dewey's critical insight and then the role of the teacher is discussed in the complexity theory. Then, the teacher’s image as an emergence facilitator is suggested instead of their im...

Probability Representation in Quantum Field Theory

The recently proposed probability representation of quantum mechanics is generalized to quantum field theory. We introduce a probability distribution functional for field configurations and find an evolution equation for such a distribution. The connection to the time-dependent generating functional of Green's functions is elucidated and the classical limit is discussed. The use of statistical ...

From Fuzzy Probabilities to Linguisti Probability Theory

A Study on Properties of Dempster-Shafer Theory to Probability Theory transformations

In this paper, five conditions that have been proposed by Cobb and Shenoy are studied for nine different mappings from the Dempster-Shafer theory to the probability theory. After comparing these mappings, one of the considerable results indicates that none of the mappings satisfies the condition of invariance with respect to the marginalization process. In more details, the main reason for this...