Mathematics Problem Archive

Let $A_1,\dots,A_n\in \mathbb{R}^{d\times d}$ be symmetric matrices and $g_1,\dots,g_n\sim\mathcal{N}(0,1)$ i.i.d.. Does the following hold? $\mathbb{...

Let $X\in\mathbb{R}^{d\times d}$ be a symmetric matrix with (otherwise) independent gaussian entries. Prove (or disprove): $\mathbb{E} \|X\| \lesssim\...

Prove or disprove the following conjecture by Feige : Given $n$ independent random variables $X_1,\dots,X_n$ s.t., for all $i$ , $X_i \geq 0$ and $\ma...

What is the partial recovery threshold for the Stochastic Block Model on $k\geq 3$ communities....

What is the exact recovery threshold for the Stochastic Block Model with a logarithm number of communities? Both computational and information theoret...

Let $S_n=S_0+X_1+\cdots+X_n$ be a renewal process whose i.i.d. strictly positive recurrence times have infinite mean and a non-lattice distribution. I...

For simple random walk $(X_n)$ on the uniform infinite planar triangulation, prove that the graph distance from the starting point has exponent $1/4$,...

Take a uniform quadrangulation with $N$ faces conditioned to have genus $CN$, where $0<C<1/4$. Prove that its rooted local limit is the stochastic hyp...