# Can random walks be applied to String Theory in curved space

• A
If we study the high temperature limit (near Hagedorn) of a string gas, most of the energy is concentrated in a single long string. If we model the string by a fixed number of rigid links of length ls and calculate the number of possible configurations, we get the density of states:

$$\omega(E) \sim \frac{ e^{ \beta E} }{ E^{ 1+D/2 } }$$

Is it possible to generalize this method in curved space?

A possible way is to calculate the torus path integral of a string that wraps the euclidian periodic time in a curved background. At high temperatures this can be calculated from the path integral of a single non-relativistic particle, which gives the free energy and thus the density of states. This seems to be called the random walk model. References: http://arxiv.org/abs/1506.07798 and http://arxiv.org/abs/hep-th/0508148 .

But this seems totally different. A particle path can be related to a random walk, but one doesn't calculate the number of microstates from combinatoric reasoning. Is there a way to do something like that?

## Answers and Replies

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?