# Tagged Questions

**2**

votes

**1**answer

59 views

### limiting empirical spectral distribution of the Laplacian matrix on an Erdos-Renyi graph?

Let $G$ be an Erdos-Renyi random graph (i.e. an edge ($ij$) exists with probability $0 < p < 1$ and all edges are independent). Let $L$ be the Laplacian matrix of this graph (i.e $L=D-A$, where ...

**2**

votes

**1**answer

344 views

### “Nice” eigenvectors for (square of) adjacency matrix of a bipartite graph?

Let $G$ be a bipartite graph, and let $A$ be its adjacency matrix.
I was wondering in this case whether $A^2$ will have nice eigenvectors that reflect combinatorial structure of the graph. I'd be ...

**14**

votes

**1**answer

577 views

### Convexity of spectral radius of Markov operators, Random walks on non-amenable groups

Let $P_1,P_2$ denote stochastic transition matrices on a countable set $I$.
Consider $P_1,P_2$ as operators on $\ell^2(I)$ given by multiplication.
Question
Under which conditions can we show that ...

**6**

votes

**3**answers

1k views

### Random bipartite graphs

Consider the following situation: I have a set $A$ of $n$ vertices and a set $B$ of $N = n^2$vertices. I consider the bipartite graph $(A, B)$ and put at random $M = n^{1 + \varepsilon}$ edges (or I ...