# All Questions

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### martingales and intersection of random walks

Let $G=(V,E)$ be a graph with $n$ vertices. Consider a pair of simple random walks $(X,Y)$ on the graph, each of length $L$ starting from a node $v \in V$. We denote a length-$L$ random walk $X$ as a ...
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### Bousfield Localization of a left proper accessible model category

What is known about the Bousfield localization of a left proper accessible model category by a set of maps ? (I mean not combinatorial which is already known)
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### Weighted inner product of independent random unit vectors

Let $u=(u_1,...,u_n)$ and $v=(v_1,...,v_n)$ be independent random unit vectors in $\mathbb{R}^n$. Let $\lambda=(\lambda_1,...,\lambda_n)$ be a fixed unit vector in $\mathbb{R}^n$. What is the ...
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### Extension of probability space problem: Hilbert space valued process V.S. random field

Maybe the question should be "Understanding the measurability: Hilbert space valued process V.S. random field" Consider the SPDE $${\rm d}u+\cdots{\rm d}t=\sigma(t,u){\rm d}W.$$ Consider the ...
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### Questions Regarding Conditional Entropy

Consider a random variable $G$ distributed in a bounded 2d plane e.g. a square. For any point $g$ sampled from $p(G)$, there are 10 points $s_i$ at the same position as $g$. Assuming all $s$ are from ...
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### Line bundles trivial outside of codimension 3

Let $X$ be a CW complex (possibly a topological/smooth manifold) of dimension $n$, $L\to X$ a complex line bundle and $Y\subset X$ a subcomplex (possibly a submanifold) contained in the codimension 3 ...
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### General formula for a conditional recursive equation

I've discovered general formulas for other recursive equations but the fact that this one is conditional stumped me. I tried approaches like using Wolfram Mathematica to try and solve it or just ...

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