What are the best books to understand Brownian motion and statistical mechanics?

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The discussion centers on the exploration of Brownian motion and its connection to the random walk problem. A user seeks book recommendations for understanding Brownian motion, particularly in the context of statistical mechanics. Suggested readings include "Lemons" for an introductory perspective, "Reichl" for a more advanced but less accessible text, and a book by Michael Plischke and Birger Bergersen that covers stochastic processes among other topics. After engaging with "Lemons," the user expresses interest in finding less rigorous materials on random walks that involve reflection and absorption, indicating a preference for accessible texts over highly technical ones. The conversation highlights the need for resources that bridge foundational concepts in probability and stochastic processes.
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I am quite well versed with the random walk problem and am interested in finding out more about Brownian motion. Does anyone have any suggestions for books that explain Brownian motion in detail? I suspect these will be books on statistical mechanics.
 
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xepma said:
I'm not too familiar with this field (at all actually), but some books that seem to get reasonable reviews are:

Lemons (introductory):
https://www.amazon.com/dp/080186867X/?tag=pfamazon01-20

Reichl (more advanced, but not that well-written)
https://www.amazon.com/dp/3527407820/?tag=pfamazon01-20

Michael Plischke, Birger Bergersen (Reasonable book; has a chapter on stochastic processes, but covers a lot more than that)
https://www.amazon.com/dp/9812561552/?tag=pfamazon01-20



Cheers.

Lemons is along the lines of what I was looking for. Thank you so much Xepma!
 
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Okay. I have nearly devoured Lemons. I would now like to know if there is some reading material on random walks with reflection and absorption. Googling seems to turn up very advanced texts and there aren't any topics here on PF.
 
I have tried reading from a book called Probability by William Feller, but I would like something a little less rigorous for now due to won't of time. If anyone has any material about the random walk problem with reflection and absorption, could you please tell me?
 

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