Lectures related to Percolation Theory

Phase Transitions: Percolation in 2D Networks

Explores phase transitions through percolation in 2D networks.

Covers bond percolation on a square lattice, discussing percolation phases, critical threshold, mean cluster size, and critical point scenarios.

FK-Percolation and the Six-Vertex Model: Critical Phenomena

Covers the transition from the six-vertex model to FK-percolation, focusing on critical phenomena and phase transitions in two-dimensional systems.

Renormalization & Scaling

Explores renormalization, scaling, critical points, exponents, and phase transitions in conformal field theory and quantum gravity.

Epidemics and Bootstrap Percolation in Square Lattice

Explores epidemics spread models and Bootstrap Percolation in square lattice networks, focusing on the Kolmogorov equation and probability generating functions.

GFF Convergence and Six Vertex Models: Phase Transitions

Covers GFF convergence and the six vertex model's phase transitions.

Universality and Rotational Invariance in Isoradial Graphs

Covers universality and rotational invariance in isoradial graphs and their implications in statistical mechanics.

Renormalization Group in Field Theory

Explores the Renormalization Group in field theory, discussing scaling functions, critical exponents, and Gaussian fixed points.

Percolation: Random Graph Models

Covers percolation theory and random graph models, exploring connectivity thresholds and critical power for wireless networks.

Turbulent State Symmetries

Explores broken and emerging symmetries in turbulent states, discussing energy cascades, lack of scale invariance, and potential conformal invariance.

Currents in the O(n) Model: Conformal Field Theory Insights

Covers the O(n) model on the hexagonal lattice and its currents.

Critical Exponents from RG

Covers CFT, gravity, phase transitions, critical exponents, and RG formalism.

Conformal Loop Ensembles: Connections to CFT

Explores the relationship between conformal loop ensembles and conformal field theory, focusing on the three-point nesting function and its mathematical derivation.

Bootstrap Percolation: Diffusion and Thresholds

Explores diffusion bootstrap percolation in networks, focusing on activation thresholds and information spread in social networks.

Complex Systems: Critical Phenomena

Explores critical phenomena in complex systems, including stochastic objects, percolation, and combinatorial optimization.

Dependence and Correlation

Explores dependence, correlation, and conditional expectations in probability and statistics, highlighting their significance and limitations.

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Renormalization Group: Universal Critical Exponents

Explores the universal critical exponents of microscopic systems and the role of the renormalization group.

Conditional Probability: Prediction Decomposition

Explores conditional probability, Bayes' theorem, and prediction decomposition for informed decision-making.

Probability and Statistics

Covers fundamental concepts in probability and statistics, emphasizing data analysis techniques and statistical modeling.