Statistical Fluctuations in the Causal Set-Continuum Correspondence

          @misc{ pirsa_PIRSA:25020040,
            doi = {10.48660/25020040},
            url = {https://pirsa.org/25020040},
            author = {Kouchekzadeh Yazdi, Yasaman},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Statistical Fluctuations in the Causal Set-Continuum Correspondence},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {feb},
            note = {PIRSA:25020040 see, \url{https://pirsa.org}}
          }
          

Abstract

Causal set theory is an approach to quantum gravity that proposes that spacetime is fundamentally discrete and the causal relations among the discrete elements play a prominent role in the physics. Progress has been made in recognizing and understanding how some continuumlike features can emerge from causal sets at macroscopic scales, i.e., when the number of elements is large. An important result in this context is that a causal set is well approximated by a continuum spacetime if there is a number-volume correspondence between the causal set and spacetime. This occurs when the number of elements within an arbitrary spacetime region is proportional to its volume. Such a correspondence is known to be best achieved when the number of causal set elements is randomly distributed according to the Poisson distribution. I will discuss the Poisson distribution and the statistical fluctuations it induces in the causal set-continuum correspondence, highlighting why it is important and interesting. I will also discuss new tools and techniques that facilitate such analyses.