We investigate the emergence of new research fields by analyzing scientific publications submitted to arXiv using

• Probability theory and random walk theory

• Population dynamics: differential form of the process of discovery

• Continuous time random walk and Levy flights: spatial and temporal characteristics of the process of discovery

Project with M. Santolini and E.Barme (CRI)

Many processes in our world can be encoded into random walk models. 

One can ask "What is the probability that two friends in one city meet each other if they do not have phones as it is shown in the figure below".

One can consider this problem from two perspectives of random walks analysis:

1. random walks in continuous space 

2. random walks in discrete space (on a graph)

What is the probability that 2 drifters do not meet or meet? 

For making 1->2 we can scrap the osm data and put this on a graph using this notebook: https://github.com/lecturers-without-borders/geo_data_analysis/blob/master/get_schools_from_locations.ipynb