Identifying statistically significant gene rich and gene poor regions
Interesting question. I don't myself know how to do this but a literature search returns some older papers on how this was achieved for pig and chicken genomes over a decade ago. The best way to do this today is to look through annotated genomes (like the mouse mm10) and use a gene density metric. You can achieve this with R code, writing your own code, trying to use some of the rich features provided in-browser at the UCSC genome browser (for mice, otherwise start here), or perhaps try to search literature for gene density stuff. I defer to others for more specialized answers.

PS. Since you're also interested in determining statistical significance, you probably will need to apply this over a sliding window across chromosome lengths, and this kind of question has been answered often elsewhere on SE (example). Sorry I can't be of more help; good luck!