I am a computer science student with a decent understanding of linear algebra and calculus. I work at a neuroscience lab where interesting results appeared with regards to the dominant eigenvalue of a random matrix $\Omega$. This matrix is an $m \times m$ binary matrix with entries in $\{0, 1\}$. Every column represents the simulation of a neuronal spike train - every row a discrete time bin. For example, if $\Omega_{35} = 1$, then a spike (or action potential) occurred in the fifth simulation at the third time instant.
On each simulation, spiking probability at time $t$ is given by a function $r(t)\Delta t$ where $r(t)$ is the firing rate of the neuron at time $t$ and $\Delta t$ the size of each time bin. Such firing rate is on its turn a function of an intricate series of factors which would be too long to describe here. Suffices to say the generation of $1$s and $0$s on each entry of $\Omega$ is random.
I have no knowledge on random matrix theory, but I deem it will be useful to acquire at least its fundamentals in view of our results. I have no knowledge of the literature on the matter. Any recommendations? Hopefully the context I've provided will be useful to the reader in providing me with recommendations more suited to my specific needs.
Thanks in advance.