Zero-One Laws for Existential First-Order Sentences of Bounded Quantifier Depth

Autor: Moumanti Podder, Maksim Zhukovskii

Publikováno v: ACM Transactions on Computational Logic. 23:1-27

For any fixed positive integer k , let α k denote the smallest α ∈ (0,1) such that the random graph sequence { G ( n, n -α )} n does not satisfy the zero-one law for the set ε k of all existential first-order sentences that are of quantifier de

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::81f44d0a3de02ce5613a2115553e232b
https://doi.org/10.1145/3489466

Random tree recursions: Which fixed points correspond to tangible sets of trees?

Autor: Moumanti Podder, Tobias Johnson, Fiona Skerman

Publikováno v: Johnson, T, Podder, M & Skerman, F 2019, ' Random tree recursions : Which fixed points correspond to tangible sets of trees? ', Random Structures and Algorithms . https://doi.org/10.1002/rsa.20895

Let $\mathcal{B}$ be the set of rooted trees containing an infinite binary subtree starting at the root. This set satisfies the metaproperty that a tree belongs to it if and only if its root has children $u$ and $v$ such that the subtrees rooted at $

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::10b837632778516336da8d5f8c055554
https://doi.org/10.1002/rsa.20895

Existential monadic second order logic on random rooted trees

Autor: Alexander E. Holroyd, Avi Levy, Joel Spencer, Moumanti Podder

Publikováno v: Discrete Mathematics. 342:152-167

We address questions of logic and expressibility in the context of random rooted trees. Infiniteness of a rooted tree is not expressible as a first order sentence, but is expressible as an existential monadic second order sentence (EMSO). On the othe

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https://doi.org/10.1016/j.disc.2018.09.012

Ruin probabilities under Sarmanov dependence structure

Autor: Krishanu Maulik, Moumanti Podder

Publikováno v: Statistics & Probability Letters. 117:173-182

Our work aims to study the tail behaviour of weighted sums of the form $\sum_{i=1}^{\infty} X_{i} \prod_{j=1}^{i}Y_{j}$, where $(X_{i}, Y_{i})$ are independent and identically distributed, with common joint distribution bivariate Sarmanov. Such quant

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::30013bd76c3c9229cda9638edc49f618
https://doi.org/10.1016/j.spl.2016.05.021

Galton-Watson probability contraction

Autor: Joel Spencer, Moumanti Podder

Publikováno v: Electron. Commun. Probab.

We are concerned with exploring the probabilities of first order statements for Galton-Watson trees with $Poisson(c)$ offspring distribution. Fixing a positive integer $k$, we exploit the $k$-move Ehrenfeucht game on rooted trees for this purpose. Le

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::452357178794b37d606e2097827f4e69
https://doi.org/10.1214/17-ecp47