On the Number of Real Zeros of Random Sparse Polynomial Systems
Abstract. Consider a random system [Formula: see text] of [Formula: see text] random real polynomials in [Formula: see text] variables, where each [Formula: see text] has a prescribed set of exponent vectors in a set [Formula: see text] of size [Formula: see text]. Assuming that the coefficients of the [Formula: see text] are independent Gaussian of any variance, we prove that the expected number of zeros of the random system in the positive orthant is bounded from above by [Formula: see text]. This result is a probabilistic version of Kushnirenko’s conjecture; it provides a bound that only depends on the number of terms and is independent of their degree.
Authors
- Máté László Telek (ORCID: https://orcid.org/0000-0001-9237-3776)
- Alperen A. Ergür (ORCID: https://orcid.org/0000-0002-2340-6551)
- Josué Tonelli-Cueto (ORCID: https://orcid.org/0000-0002-2904-1215)
Institutions
- University of Copenhagen (DK)
- Budapest University of Technology and Economics (HU)
- CUNEF Universidad (ES)
- The University of Texas at San Antonio (US)
Publication Details
- Journal
- SIAM Journal on Applied Algebra and Geometry
- Published
- 2026-10-29
- DOI
- https://doi.org/10.1137/25m1734191
- Primary Topic
- Polynomial and algebraic computation
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- University of Texas at San Antonio
- European Commission
- Banff International Research Station for Mathematical Innovation and Discovery
- European Research Council