As an AI language model, I don’t have live data access. The list of cities with the most start-ups per capita can vary depending on the source and timeframe. However, I can provide you with a list of cities that are frequently mentioned as having vibrant start-up ecosystems. Please note that the rankings might change each year:
1. Silicon Valley, USA
2. Tel Aviv, Israel
3. Berlin, Germany
4. London, United Kingdom
5. New York City, USA
6. Singapore, Singapore
7. Stockholm, Sweden
8. Sydney, Australia
9. Toronto, Canada
10. Seoul, South Korea
Keep in mind that there are many other cities around the world with thriving start-up communities that are constantly evolving. Additionally, rankings can differ based on various factors like investment, tech infrastructure, government support, and more.