| Apr 17, 2025 |
The Column-Row factorization $(A = CR)$ We describe how every matrix $A \in \R^{m \times n}$ with rank $c \geq 1$ can be factorized into $A = CR$ where $C \in \R^{m \times c}$ and $R \in \R^{c \times n}$. |
| Jan 26, 2025 |
Why play Langur Burja with Six 6-sided dice We consider how the game would vary if it was played with a different number of dice, or with a different number of symbols. We empirically observe that the number of faces in the dice should be greater than or equal to the number of dice for a House advantage. |
| Jan 19, 2025 |
The rules of Langur Burja We state the rules of this popular Nepali betting game. We consider some alternate payoff schemes and argue against them. |
| Sep 28, 2024 |
Taking Markov Steps We walk through a simple example of a random walk on a finite graph. |
| Sep 18, 2024 |
Existence and Uniqueness of The Stationary Distribution Assume a finite irreducible and aperiodic Markov Chain $\{X_t\}_{t \geq 0}$ with transition matrix $P$. We prove, by construction, the existence of the stationary distribution $\pi$ for every such Markov Chain. |
| Sep 18, 2024 |
Notation for Markov Chains A post containing the notation for all Markov Chain posts on this blog. |
| Aug 26, 2024 |
Lower Bounds on Markov Chains - The Counting Bound We follow the exposition of Levin and Peres to describe the counting bound, which is a way to lower bound the mixing times of Markov Chains. |
| Jun 29, 2024 |
Parsing the Cutoff Phenomenon We introduce the Cutoff Phenomenon, observed in some Markov Chains, and show how one might go about defining it. |
| Mar 30, 2024 |
ReLu NNs to compute some basic functions We construct ReLu NNs that that compute the addition, maximum and absolute value functions. |
| Oct 21, 2023 |
Some notes on Lawler's 'Expected hitting times of a random walk on a graph' My notes on this already very readable paper. |
| Jul 8, 2023 |
Kicking off this blog A short, hope-filled post to kick-off this website. |