Probabilities of small deviations of a critical Galton-Watson process with infinite variance of the number of the direct descendants of particles

Key Points

• The research aims to understand the small deviation probabilities for a critical Galton-Watson process with infinite offspring variance.
• Analyzed the asymptotic behavior of small deviation probabilities.
• Investigated a reduced critical Galton-Watson process under a small deviation assumption.
• Identified specific characteristics of small deviations in the process.
• Showed how these deviations influence the structure of the critical Galton-Watson process.