Bounds on Probability and Chebyshev's Inequality in Probability and Statistics
Explore Chebyshev's Inequality, its derivation, and practical applications in probability and statistics for engineering and business students.
Branching Processes for Cascades on Networks
Explore branching processes and their application to network cascades, gaining insights into complex system dynamics and interdisciplinary physics concepts.
Conditioned Exit Measures of Non-Local Branching Processes
Explore conditioned exit measures of non-local branching processes in this mathematical conference talk by Emma Horton at CIRM.
Accessibility Percolation for the Rough Mount Fuji Model
Explore accessibility percolation in the rough Mount Fuji model through a mathematical conference talk by Matt Roberts at CIRM.
On the Extinction Time and Maximal Displacement of Critical Branching Killed Levy Processes
Explore critical branching killed Levy processes, focusing on extinction time and maximal displacement in this mathematical analysis.
Analytic Insights into the Zig-Zag Product and Its Friends - Part I
Explore advanced graph theory with Gil Cohen, delving into the Zig-Zag product and related graph operators using innovative analytic techniques for more precise bounds and insights.
Analytic Insights into the Zig-Zag Product and Its Friends - Part II
Explore advanced analysis of graph operators using full spectrum and analytic techniques. Gain insights into Zig-Zag product, derandomized squaring, and their optimal bounds through finite free probability and analytic combinatorics.
Subgroup Tests and the Aldous-Lyons Conjecture
Explore the refutation of the Aldous-Lyons conjecture through novel interactive proof systems and subgroup tests, connecting complexity theory to probability theory and group theory.
Geometric Representations of Far Future Predictions in Deep Neural Networks - Next-Token Training
Explore universal geometric representations of far-future beliefs in deep neural networks trained on next-token prediction, uncovering fractal and quantum-like structures embedded in network activations.
Yudovich Theory for Rough Path Perturbations of Euler's Equation - Lecture 2
Delve into Yudovich Theory for rough path perturbations of Euler's equation in this advanced lecture by Torstein Nilssen, exploring mathematical aspects of fluid flow equations and recent developments in the field.
Know When You Know: Handling Adversarial Data by Abstaining
Explore sequential prediction in stochastic settings with adversarial interference. Learn strategies for handling distribution shifts and making confident predictions while abstaining from uncertain cases.
The Fundamental Group of Random 3-Manifolds and Other Random Objects
Dive into the fundamental group of random 3-manifolds, exploring probability distributions and their applications to various categories in mathematics.
Mathematical Snippets From Developments in AI
Explore mathematical insights arising from AI developments in this colloquium by Lek-Heng Lim, examining key observations and their implications for the field.
Stochastic Quantisation of Yang-Mills
Dive into stochastic processes and Yang-Mills theory with Martin Hairer's talk on building a process admitting the 3D Yang-Mills measure as its invariant measure, exploring gauge-covariance and UV regularization.
A Descriptive Approach to Pointwise Ergodic Theorems
Dive into a descriptive approach to pointwise ergodic theorems, exploring their applications in dynamical systems, probability, and number theory.
Random Planar Geometry and the Directed Landscape
Dive into random planar geometry and the directed landscape, exploring universal scaling limits in random metrics and interface growth models with Duncan Dauvergne.
Dimension of Stationary Measures - Lecture 3
Delve into the dimension of stationary measures in random walks on matrix groups, exploring flag spaces, Oseledets measures, and configuration space dynamics. Gain insights into entropy and dimension addition.
Dimension of Stationary Measures in Random Walks on Matrix Groups - Lecture Series
Explore the dimension of stationary measures in random walks, focusing on matrix group actions over flag spaces. Gain insights into exact dimensions, partial answers, and the intricate structure of flag spaces.
Dimension of Stationary Measures - Lecture 2
Explore the dimension of stationary measures in random walks, focusing on matrix group actions over flag spaces. Gain insights into exact dimensions, partial answers, and the intricate structure of flag spaces.
Dimension of Stationary Measures - Lecture 4
Delve into the dimension of stationary measures in random walks on matrix groups, exploring flag spaces, Oseledets measures, and configuration space dynamics.
Integral Means Spectrum: Examples of Exact Computation
Explore the multifractal spectrum of harmonic measure and integral-means spectrum of Riemann maps through explicit computations in deterministic and random cases.