Criticality transition for positive powers of the discrete Laplacian on the half line Gerhát, Borbála M Krejčiřík, David Štampach, František ddc:510 We study the criticality and subcriticality of powers (−Δ) α with α>0 of the discrete Laplacian −Δ acting on ℓ 2 (N). We prove that these positive powers of the Laplacian are critical if and only if α≥3/2. We complement our analysis with Hardy-type inequalities for (−Δ) α in the subcritical regimes α∈(0,3/2). As an illustration of the critical case α≥3/2, we analyze asymptotic properties of discrete eigenvalues emerging by coupling (−Δ) α with a localized potential. EMS Press 2025 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/19642 https://research-explorer.ista.ac.at/download/19642/19656 Gerhát BM, Krejčiřík D, Štampach F. Criticality transition for positive powers of the discrete Laplacian on the half line. <i>Revista Matematica Iberoamericana</i>. 2025;41(3):1173-1200. doi:<a href="https://doi.org/10.4171/RMI/1523">10.4171/RMI/1523</a> eng info:eu-repo/semantics/altIdentifier/doi/10.4171/RMI/1523 info:eu-repo/semantics/altIdentifier/issn/0213-2230 info:eu-repo/semantics/altIdentifier/e-issn/2235-0616 info:eu-repo/semantics/altIdentifier/wos/001476507600013 info:eu-repo/semantics/altIdentifier/arxiv/2307.09919 https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess